Borderline for 720 streaming flash video, too low for 1080.
Best bet is to download the video first then watch it from your hard drive, or use one of the many Youtube viewers/browser plugins/etc. In other words don't use Adobe Flash Player if performance is your goal.
And of course make sure you've installed the optimum video drivers for your card. That can make a huge difference in video performance! I am not an ATI expert but they have good documentation in the Debian Wiki.