First answer: I'd personally go for the XFX Radeon HD5770. It'll handle just about anything you throw at it, and (with the possible exception of Crysis) you'll be able to achieve some Hi-Def gaming with plenty of eye candy.
The 4890 isn't a bad card, but personally, I like the idea of future-proofing. Not to mention the 4890 is freakin' huge and power-hungry
Second answer: The advantages of the 5xxx series of Radeons include not only DX11, but Eyefinity, ATI Stream (similar to nVidia's CUDA), and Dolby TrueHD and DTS-HD Master Audio support. Not to mention it's lower power draw and operating temperatures vs. the previous generation of GPUs. The cards are also physically smaller than the previous generation, making it easier to fit it into almost any case.
The only real advantage to the GTX260 is if you want to run PhysX in certain titles, or you're playing a game that supports 3D-Vision and have the rest of the equipment to go with it. Personally, I don't think it's worth it.
Hope this answers it for you.