If your primary concern is an antelope and deer rifle then the .243 would be my pick. An 85 grain BTHP out of the .243 is some dang fine antelope medicine. Does a pretty darn good job on bigger deer also.
Concerning target shooting.... A 6mm bullet will punch a hole in paper just like a .308 bullet. Neither one is going to be more or less accurate than the other on average.
Since you live in Colorado the .243 would also make a fantastic prairie dog and coyote cartridge with the 55 grain bullets available.