What are the differences between the iOS and PC/Console versions of XCOM, if any?

Solution 1:

As you have already found, one of the main differences is the drop in graphics quality. This means, according to Pocket Gamer:

• Lower resolution
• No mouth animations
• Fewer dynamic camera angles (kill cams, presumably)
• Lower quality lighting

Additionally, the PvP multiplayer mode is not available. However, according to both Venture Beat and Joystiq, it will be added at a later date.

There's an interview with Jake Solomon, the lead designer, stating

"The amazing thing is that all of the gameplay is there, and we just had to trim a few maps in order to get it to work on mobile."

and

"The interface has been changed slightly, taking the PC interface as the starting point.

As for the DLC, in Joystiq's announcement article they say that the Elite Soldier DLC is included but that the Slingshot DLC is not. As far as I can see, the Second Wave patch is similarly not included.

Edit: A recent patch has added the Second Wave options to the iOS version (thanks to bpcookson for the heads up).