For playing back video either will be fine. Actually, a dual core would be fine. If you buying new parts to make the HTPC, then consider AMD's Llano APU series or the Intel Core i3-2100 thru i3-2125 CPUs. Those CPUs have integrated graphic cores which means you don't need to buy a video card.
If you encode your own videos, then the Phenom II would be better. Again, if you are buying new parts, you might want to consider the Core i5-2300, 2310 or 2400 depending on your budget. The Core i5 series offers better video encoding performance than the quad core Phenom II X4 series.
An X3 does well. I found the athlon x2 240 a tad sluggish and replaced it with an x3 445 a year ago and am happy with that. My motherbd has an integrated radeon 4250 that has dedicated memory and handles the video aspects just fine.
My newer build uses an i3-2105 which I find to be even more responsive than the AMD x3. Its integrated hd3000 GPU handles the video just fine also.
+1 to all the llano recommendations. The llano APU's from AMD have built in GPU's comparable to decent entry level dedicated graphics and FAR superior to any integrated GPU's intel has to offer. These chips are a great choice for an HTPC lowering cost, voltage/heat/noise and case size all the while providing more power than you would need in an HTPC.
I've done both and didn't have a problem with either. I kind of liked the quad core Phenom II a little better than the athlon. I agree with pop the Athlon seemed a little slow in loading movies but it was still ok.
Lack of a L3 cache woudnt be a bother since your main purpose seems to be building a HTPC. So Athlon is a better one out of these two. But the Ilano processors have better graphics which would help you in video decoding. Im not sure about the editing and transcoding performance of Ilano but Im sure they are much below Intel HD 2000\3000.
I'm not quite sure what supersdu means by editing/transcoding performance as this is a task handled by the CPU in which a llano CPU priced equally to an intel will be a quad core CPU vs. a dual core on the intel side and there in clearly more suited to tasks of this nature.