I've sinewed many bows with sinew from various animals. Speaking strictly LEG sinew, the main difference to me is the texture. I've observed that Buffalo sinew processes and lays real nice, almost silky on a bow. I would say that cow sinew is probably next smoothest. Then next down the line might be Whitetail and Elk. I used Caribou sinew also. I've found it to be more course in texture. It didn't lay as nice and the cured end result wasn't as smooth. I am accused of being a bit of a perfectionist and it bothered me some, aesthetically. I tried Ostrich sinew a long time ago. I didn't like it. I don't remember why, just didn't care for it. Maybe, it was just too long?
As far as performance, I've found no noticable differences between any of them.
Just, my two cents...