7900 and 5700/6700 are NOT. At least not fully. Front mech pull ratio is way off and (IIRC) using 7900 shifters with a 5700 mech means you need to put a stupid amount of force through the lever to get it to shift.
I got 7900 FD with 6700 shifters... Is that why I'm always rubbing 1-2 gears when cross-chained? I "upgraded" to 7900 and moved the 6700 FD to my TT bike..
( you CAN however, run a sram shifter with a shimano front derailleur or a shimano shifter with a sram front derailleur.)
brakes between sram and shimano are cross compatible as well.
I assume this DOES NOT apply for SRAM Red 10s with the new Yaw FD? I think I'm going to change out the whole shifting system to SRAM soon, the rear shifting doesn't feel crisp at all. The lever action just feels loose and plasticky.