So are you asking which is the better card for gaming? The Radeon 5770 or the Radeon 4890?
Well, for performance, the Radeon 4890 is definitely faster at stock. But it has very little overclocking headroom.
While the Radeon 5770 is only about as fast as the Radeon 4870, but it is a whole lot more overclockable than the Radeon 4890, not to mention lower power consumption and Direct X11 support as well.
If you only care about performance, get the 4890, if you want flexibility plus features like Direct X11, which can help in longer shelf life of your video card. Then choose the Radeon 5770.