Which is better ATI Radeon HD 4200 or 4250

The 4250 is slightly better, but it is not a huge difference. It has a clock rate of 560MHz / 40GFLOPS opposed to the 500MHz / 44.8 GFLOPS of the 4200.

To give you a better idea of how they compare, the 4200 has a Pixel filtrate of 2 GP/s, a Texture fillrate of 2 GP/s and a FP32 of 1 GP/s. Where the 4250 has a a Pixel fillrate of 2.24 GP/s, a Texture fillrate of 2.24 GP/s and a FP32 of 1 GP/s.

If you don't play graphically intensive computer games, do 3D design, or video transcoding and all you really want it to do is make GNOME or KDE or Aero look sexy, it should work just fine. They both provide full 1080p and offer UVD2.

All that said, they both support something called side port memory. The motherboard mfg can put up to 128 MB of extra memory on the motherboard that the Radeon can use for it's frame buffer. Some models have it and some do not, you would be more likely to find it on a higher end model. So take that into account with comparing boards.