I bought a new 27" 2560x1440 monitor and needed something beefier than my integrated Radeon HD 4XXX.
I went with a 7770 because it appeared on Tom's Hardware's best graphics card for the money December (its still there for January too).
I was going to get the best one for under $100 but I saw this one for $125 and was supposed to be a lot better.

It may be better on paper or under Windows, but I don't use my graphics card on paper or on Windows... I run Linux.

I tried this 7770 under Ubuntu 12.10 and Linux Mint 14.
I tried both both the open source then the proprietary drivers under Unity, Cinnamon, and XFce.
I installed all the vaapi stuff to get hardware accelerated video. I used a special mplayer from some ppa and the vlc seemed to be able to work with hardware if I just checked a button.
In any case.... 1080P Bluray rips in mkv format (not transcoded, the entire 25-30Gb files) where very CPU intensive and had tearing under CPU rendering and glitches under hardware rendering.
I have the same 1080P rips transcoded down to 2-3GB files at 720P for my phone and Nexus 7 in H.264 as mp4 files... those still had tearing under CPU and showed a lot of glitches with hardware rendering.

When I get home today I will try their latest 13.1 catalyst drivers and if that doesn't solve all of my problems I think I'll go the NVidia route.

Will I have more luck under NVidia than I will under AMD as far as tear-free 1080P video playback?

Its pretty sad when my $300 phone and $200 tablet can handle HD Videos but my 6-core 3.2GHz desktop with a $125 graphics card and 8Gb RAM can't handle it.