With a Stampede you will blow the transmission up with a 7700 in it pretty easily. With a 15T motor in my neighbors and with the hobbyshop demo Stampede we melt the spyder gears. If you don't mide replacing some gears from time to time and want as fast as they come then get the 7700.
For the TA04 you shouldn't have any real problems as long as you have the proper gear mesh and the diff is set correctly. The 7700 with be insanely fast for what you looking to put in. Hold on.