"low power consumption" is relative. The 46xx have a low power consumption and should be powerful enough for movies, compositing and older games. 5770 is only needed if you're either into 3d modeling/rendering or simply into recent games.
To avoid tearing, you'd have to display the movie using openGL. xv will tear. I've had a bit of gfx corruption when switching to fullscreen with ogl, so I still use xv. (as a multiscreen-user, my movies will tear anyway.)
You could try xvba, if you can get it working. I didn't bother.
Games on windows are just beautiful with the card and a high-res monitor

The 5770 is more powerful than anything in current-gen consoles (360/ps3/wii), so anything working on those consoles should run great. (unless the game was ported by a bunch of typewriter-monkeys, but let's not talk about GTA IV here)
Games on Wine, see above. It all depends on the games, some work great, some work with minor flaws, some suffer heavy performance penalties and some don't work at all.
http://appdb.winehq.org is your friend.
I've had a few stability problems with fglrx. Not more often than previously with the nvidia drivers, but more severe: nvidia just killed the X server, fglrx hangs the whole system (thus taking a minute longer to recover). Annoying, but I only regard fglrx as a necessary evil until OS support arrives, anyway.