The following is a list I compiled highlighting many of the different features of the two.
Graphics

FSX
-DirectX9
-Supports worldwide terrain with 14 GB of scenery information
-scenery objects for most major cities
-auto generates trees and buildings for filler
-high quality reflective water
-highly detailed aircraft and 3D cockpits for all default aircraft.
-can use multiple monitors
X-plane 9
-OpenGL 2
-Worldwide terrain with 70 GB of scenery information
Has a higher resolution terrain texture.
DOES NOT come with scenery objects such as cities and airport buildings but these can be downloaded off the web for many airports. If you load at an airport with default scenery, there will be runways, taxiways and tarmac but no buildings. The demo area is an example of what can be added as scenery files.
- Highly detailed aircraft
- 3D cockpits for SOME default aircraft.
- will only use multiple monitors if using Matrox DualHead2Go, or using networked computers.
- Reflective water
Flight Model
FSX
-Aircraft performance is based on configuration files and variables given to the simulator before it flies.
X-Plane 9
-Flight model is based on aircraft geometry using blade element theory and engine performance variables. Wings are broken in to sections and based on the shape of the wing, airfoil shapes, and locations, flight model is determined.
-Higher quality flight model results from this and also allows for a built in aircraft design software. Make any airplane shape you want and see how it flies.
Interface:
FSX:
-Starts at a setup window, where there are options to setup a flight, read a tutorial, view pilot stats, etc.
-In-flight, the Alt key will bring up a menu where much of the flight setup and view options can be changed.
-Cockpit knobs and buttons in both 2D and 3D are clickable and can be mapped to a key or joystick button.
X-plane 9
-There is no setup screen. It put you directly into an aircraft. The program will start at the last airport you landed in the last aircraft you flew in. From there, a menu bar at the top is available to access all flight set up options, (aircraft, location, weather).
-Cockpit knobs and buttons are clickable in 2D and 3D cockpit modes.
ATC and other aircraft
FSX
-The amount of air traffic can be set in the options screen and FSX will generate traffic to fill the airspace accordingly.
-ATC is somewhat realistic but has problems with certain things like separation. There are a few different voices that can be selected and don't sound completely like a computer.
X-Plane 9
-User specifically selects how many aircraft they want in the airspace at any given time. This traffic can be dragged around on the map by the user. The traffic seemingly randomly and does not follow normal flight patterns.
-ATC sounds like a robot but has more available commands, one example: declaring an emergency. ATC will also watch your speed and do things like tell you to slow down if you are going more than 250kts below 10000ft.
-ATC does not talk to other aircraft.
Failures
FSX
-Crashing, overspeed, overstressed simple just stops the simulation
-Systems can be failed individually
X-Plane 9
-Crashing ends simulation
-Overspeed and Overstressing cause failures of parts of the aircrafts. Wings and flaps are damaged and fall off.
-Parts of systems can be failed. Don't just fail the engine, fail the drive shaft or ignition...
FSX features that X-Plane does not have (by default):
-learning center
-tutorials and pilot lessons
-missions
-built in multiplayer
-in game Garmin GPS features
X-Plane features that FSX does not have(by default):
-Fly on Mars
-Scenarios such as: space shuttle re-entry, X-15 drop from B-52
-Airplane maker, airfoil maker, world maker
-Flocks of birds that damage plane
-ability to interface with a physical Garmin device