I'm running 6700 shifters with an otherwise all Ultegra SL group.

Rear shifting is good. A tad less smooth than with my Ultegra SL shifters. Every now and then shifting from larger rear cog to smaller results in a two cog shift or a delayed shift. I've become accustomed to priming my shifts by first moving the lever to eliminate what I consider the excessive throw, then engaging the shift. When I do this rear shifts are just as good as with my 6600 shifters.

OTOH, front shifts are fantastic. Much better than with the Ultegra shifters. Almost instant. And very crisp. I did a bit of research online before purchasing and can say that others have experienced the same.

I'm not sure how they would work with 7800, but they work quite well with 6600. Of course, YMMV.