Features in Common

In brief: both are multi-platform and are protected by the GPL. Inkscape is free software; so is part of Xara Xtreme 3 (the renderer part of Xara is still closed and binary-only) but not 4.

Inkscape Advantages

Fundamental

completely free and open source (Xara Ltd. refuses to open-source its renderer library)
open, text-based, XML-based standardized format (the Xar File Format is a published standard too, but not XML, and not widely adopted)
scriptable (rich command line)
extendable (perl/python extensions)
more localisations
ports for OSX and other Unixes, apart from Windows and Linux; all ports have the same functionality (Xara's Linux port is stagnating, only Windows version is being developed)

Features

smoother and more powerful bitmap tracer
live XML tree editor
gaussian blur (not the same as feathering; blurs everything, can be squeezed and rotated)
other generic filters (turbulence, composite, displacement map, etc), ability to compose filter stacks
live clones (copies that are linked to the original and update when it's changed)
clone tiler (can be used for two-dimensional object scattering with randomization and coloring)
tile tracing (tracing anything by a pattern of clones)
unclumping (two-dimensional, incremental equidistant distribution of objects)
randomizing object positions
paint bucket tool to fill any bounded area with a path
3D box tool [not the same as Extrude that gives photorealistic rendering of individual objects; rather, this is a building block of coordinated 3D scenes]
eraser tool
tweak tool to push, inset, outset, roughen paths and to paint/jitter colors
live path effects (pattern on path, sketch, various deformations, geometric constructions), stackable and applicable to groups
Spiro splines (more convenient than Beziers)
Open Clip Art Library (OCAL) integration [Xara can download stuff from its own site only]
baseline snapping, alignment, distribution
find dialog (find any object by type, style, id, etc)
persistent per-object export hints (filename, resolution)
export and conversions from command line, including batch export with GUI and commandline [Xara has batch export via GUI only, using Names gallery]
command line query options to examine objects in a drawing
command line access to verbs (commands) to automate tasks
hierarchical layers, "enter group" command making it a temporary layer
pattern fills from arbitrary objects; stock vector patterns
gradients/patterns on stroke as well as fill
gradient handles can be multiple-selected, selected by marquee, Alt+dragged to smoothly shape, copy/paste styled; gradient can be simplified to remove extra handles
transform/not transform switch for patterns and gradients
switch to preserve rounded rect corners in transforms
scale/rotate/skew any number of objects separately, each around its own center
numeric skew (both axes; by angle, %, displacement)
editing transform matrix
persistent per-object rotation centers
pasting of size, width, height
simplify-like deletion of nodes
node sculpting
symmetric nodes
different star/polygon rounding (both Xara's and Inkscape's approaches have their advantages)
randomized stars
spirals
easy segment and arc from ellipse
the ability to combine color and transparency in a gradient
linked offsets and text-on-path remain freely transformable
convenient calligraphy pen (sensitive to tablet pressure/tilt, speed and direction, with tremor/wiggle)
guided drawing, tracing background in calligraphic
flowing text into arbitrary shapes, chaining, exclusion
one-command removal of kerns from text
rotating characters in text (including text on path)
connector tool for diagrams
automatic diagram layout
removing overlaps
extensions for paths: randomize, add nodes, swirl, fractal, function plotter and many others
extensions for colors (inverse, more saturation, replace etc) and text (sentence case, randomize case, replace etc)
extensions for rendering barcodes, function plotter, L-systems, and many others
icon preview
masks separate from fill
vector import of PDF and CS AI (Xara either fails or imports by rasterization)
autosave

convenience

overall, times more keyboard shortcuts than in xara
a large part of all keys are configurable (including Xara emulation option) via an XML config file
keys for canvas scrolling (with acceleration)
keys for scaling and rotating (including pixel-size)
keys for scaling and rotating (including pixel-size) of nodes, including scale/rotate of node groups
keys for letterspacing, linespacing, kerning in text (including pixel-size)
nodes can be moved with snapping along the adjacent straight line segments or their Bezier controls
more snapping options, on-canvas snapping indicator
gradient handles can merge and unmerge
history of zooms (Xara has a single "previous zoom")
zooming by single key (+/-, without ctrl)
any kind of zooming (including area) without tool switching
"bounding box" per-object selection hints
cursor changes over selectable objects
node tool optionally highlights mouseovered paths
more precision in editable numeric fields

Xara advantages

fast renderer
blends [Inkscape has limited path+style blending via Interpolate extension]
envelopes, including curvilinear and perspective [Inkscape has non-interactive analog via Envelope and Perspective extensions; also non-perspective destructive distortions can be made via node sculpting or tweak tool]
linked colors
Pantone colors
Photoshop plugins/Live effects
integrated Picture Editor for embedded bitmaps
brushes along path can be used for object scattering with randomization [Inkscape's pattern-along-path LPE has no randomization]
variable stroke width, with selectable profiles or taken from pressure sensitivity [Inkscape can do this via pattern-along-path LPE]
feathering objects' edges (not the same as blurring - only inward from edge, like a blurred transparency mask) [can be emulated in Inkscape via clone+blur+mask]
more gradient types (conic, 4-point etc) [a limitation of the SVG specification, only linear and radial are defined]
bevel tool (outer/inner; join types; size; light angle and elevation; flat/rounded/chiseled etc types (15 in total)) [some of this can be done in Inkscape via filters]
"nav bar" tool for buttons (hidden in Xtreme)
quick transparency gradients separate from fill [to some extent, can be emulated by SVG masks]
gradient profiles [SVG limitation, in Inkscape can be approximated by multistage gradients]
rainbow/alt-rainbow gradient options
different star/polygon rounding (both Xara's and Inkscape's approaches have their advantages)
some input and output formats that Inkscape does not support, including Flash; but not yet SVG
non-AA display mode (note: anti-aliasing is _not_ a significant factor in the speed of Inkscape)
linked stretching (autoscaling objects), e.g. stretching button to fit the text

3.2 features:

Integrates with external photo editors
MS Word copy/paste
RTF, raw photo import
- RTF import can be done via GTK APIs. Raw photo import should use dcraw, or code derived from dcraw.
PDF-X export
XPS import/export
- This a royalty-free XML-based PDF replacement format from Microsoft. There is FOSS support for it, i.e. in Okular for KDE4.
Multipage
Text tool: paragraph spacing, snapping to pixel grid, soft hyphens, smart quotes
PSD import/export
- Would require reverse-engineering Photoshop, as there is no published specification
Flash animations
Color separations
- This means producing copies of the original image, each one containing one of the channels. This should probably be postponed after the Cairo move.

Version 4 features:

3D extrude tool with 3D rotation and lighting controls
HTML export with images
text flow around shapes
text underline
optional Adobe-like rubberband selection - objects that are touched by rect
live selecting while dragging
fonts grouped into families in Font list
key shortcuts customizable

Per-feature comparison:

Rectangle tool:

Xara:

Corner curves must be the same on each side of a corner, but then stretch if the object is resized. The curvature units aren't either percentages or pixels...?
Can create with rotation ("Radius creation" and "Diameter creation" options)
Can edit centre X/Y numerically
Can convert to ellipse by doubleclicking center

Inkscape:

Preview as-you-draw
Corner radii only in absolute units
A switch to preserve corner radii in scaling

Rotation centers:

Xara:

BAD: looks like once you move a center of an object, ALL objects will use the same center!
BAD: does not survive save/reload - all objects are reset to geometric centers. (In other words, the center seems to be the property of the Selector tool, not of objects!)
with Ctrl, center snaps to corners/midsides

Inkscape:

Each object has its own center; if you want to rotate multiple objects around one center, just select them all (taking the object with the center first)
Centers persist through save/reload
Centers snap to edges and corners/midsides

Bitmap tracer:

Xara:

BAD: all parameters are set in some relative values in the range 1..100, except for "number of passes" which does not correspond to anything quantifiable. There's no way I could find to set explicitly the number of colors.
BAD: as a result, tracing a simple line art such as a two-color logo is nearly impossible. Xara almost always creates a bunch of dirt at the fringes due to antialiasing, and shapes get distorted a lot. The Monochrome option seems to be broken.
BAD: for photos, there's no stacking option, so full-color traces come out very untidy. The shapes are also more distorted than in Inkscape. If you try to make them less distorted, they start getting pixelated.

Pen/shape editor tool:

Xara:

with the pen tool you can drag curve and nodes (with snapping and closing) while the tool is active but, strangely, not node handles. with the shape editor tool the handles can be moved and new points also added

Inkscape:

live preview of the next segment (exists in Xara when clicking/holding and dragging with the shape editor tool)
you can create hor/vert straight line segments with Ctrl (the same in Xara but only with the shape editor tool)
length/angle display in statusbar (again, in Xara only with the shape editor tool)
you can easily create disconnected subpaths (starting with Shift)

Path simplification:

Xara:

slider for the just-drawn freehand line (only), to refit both ways (looser or tighter) while it's still selected
interactive 0-100% slider in Node tool, looser only but remembers setting while you have the same nodes selected lets you de-simplify back
works on selected nodes (actually, ONLY works on selected nodes)

Inkscape: