For the HP50 vs. HD650, you are looking at reviews that are coming from very different perspective. The HP50 is a closed headphone, and closed models tend to have lower SQ and soundstage than open models. The HP50--compared to other closed models--has a very good soundstage and good SQ, so it is only natural that it would get positive reviews. Just keep in mind that they are all qualified by the fact that this is a closed model, and most open models will do better at both.
There are also two major concerns/issues I see with the HD650:
1) The HD600. Prices are lower now, but the HD600 was selling for $400, and the HD650 for $500. Most listeners find these models to be very similar, so for that price delta, it doesn't make much sense spending $100 more when the HD600 has most of the characteristics.
2) Both the HD600 and HD650 are neutral, well-rounded models. This is both their strength and weakness. You can find other models that offer more bass, or more detail, or with better efficiency (eliminating the need for an amp), but those models are pretty much guaranteed to have some other drawback. The HE-400, for instance, is a very accurate headphone with stronger bass, but it also has some harsh treble (at times) and recessed mids compared to my HD600.
See, the criticism of the HD650 (and pretty much any "audiophile" class headphone) comes down to taste, as cel mentioned. You can find all sorts of models that have slight variation from others, and in the end, the only thing that matters is whether or not you like how it sounds.
The HD600/650 is probably the best choice for you right now because you don't seem to have a lot of experience with headphones in this class. Obviously, if you can try before you buy, do it. Otherwise, these are middle of the road, well-rounded headphones that will sound great with anything you throw at them, and you can use either as the measuring stick for other models (at least in this general price range).
PS. Oh and I cannot stress enough that these models need an amp. If you just hook them up to the headphone jack on your phone or computer, they aren't going to sound very good (or not nearly as good as they will with a proper amp).