AMD decided to mix things up a bit when they released the HD6000 series first by releasing the midrange cards first and next by using previous high end naming schemes to describe them. So while the HD5870 was the previous generation "bad-boy" the new HD6870 was nothing more than a docile pony designed to give the nVidia GTX 460 some company.
Slow computer got you down? Maybe a hardware upgrade should be in your cards, if so this guide to the Fundamentals of Upgrading a PC is an invaluable read. PCSTATS Tips