Generally speaking, any Intel Ivy Bridge CPU or AMD Trinity APU has a graphics core that can handle HD video playback. AMD's FX series CPUs lacks integrate graphic cores so for that CPU you will need to buy a graphics card.
For a HTPC I generally recommend an Intel Core i3 (such as the i3-3220) over AMD's Trinity APU because of lower power consumption. Intel CPUs are also more powerful than AMD APUs and CPUs. However, for the price of a dual core i3-3220 you can buy a quad core Trinity APU. As for which integrated graphic core offers better video playback quality... that I cannot answer. The safe assumption is that AMD's Trinity APUs may offer better video quality.
Buying either an Intel Ivy Bridge CPU or AMD Trinity APU will at least allow you to initially forgo purchasing a video card if you decide that the video playback quality is good enough.
Since you mentioned video compression, I assume you will want to encode video as well. If that is the case, then choosing the correct CPU (or APU) can help reduce the amount of time necessary to encode video.