The Fastest Turion II Ultra at 2.6ghz (the M660) is only as fast as a Core2Duo at 2.26ghz. That doesn't take into account Intel's i3,i5, and i7 CPUs all of which are faster than the Core2Duos clock for clock.
Now, all that is performance wise. If you just need a laptop for basic word processing and internet surfing and maybe some mild gaming, the Turion II will be fine. Though the specific model you are looking at would be helpful.