Depends on the game. Some (most) games don't even have DX11 support.
Even with the ones that do, only a few will you see a big differences in graphics quality, Metro 2033 for example, and of course DX11 benchmarks.
DX11 is still immature, however the possiblies of DX11 are amazing, and in the future there will be a very big difference between DX11 and DX10.
The difference is a DX10/DX10.1 card cannot display DX11 graphics.
Gaming wise, the difference in graphics depends on how it is implemented by the developer. Example:
Resident Evil 5 and Devil May Cry 4 are both advetised as DX10.1 or DX11 games (I can't remember off the top of my head). However, when compared to DX9, there are no differences in the graphic effects. But playing in DX9 mode results in higher performance.
The developers of RE5 have stated that while the game does include DX10.1/DX11 coding there were no additional effects implemented. As for DMC4, the developers made no comments regarding if anything has been added. It seems DX10.1/DX11 coding had been added so the games can be adveristed as "DX 10.1" or "DX 11" games.
The main difference is that DX10 is an even number and DX11 is an odd number (don't make that face, bear with) and traditionally the odd numbered versions of DX have been better and lasted longer than the even numbered ones.