The Beats are awful. I've heard them at BestBuy, the Apple Store and at Monster's table at CanJam. I cannot find a single redeeming quality in the Beats. Scratch that. The people running the table at CanJam were nice, so I like the promoters. Other than that, I can't think of anything nice to say.
I owned the HD-650 for a bit over three years. They're not perfect and you'll find some well-reasoned critiques of them. However, the HD-650 is a terrific headphone with excellent performance top to bottom. I sold mine to finance the HD-800, not because I didn't love them.
The HD-650 will give you a wonderful introduction to audiophile sound. Once you get hooked on that, you'll wonder how you ever managed to listen to anything less.
The Beats, on the other hand, are simply a mass-market product with every bit the appeal of a generic can of beer. Or perhaps malt liquor is a better comparison. Like malt liquor, the Beats have a single-minded purpose: phenomenal amounts of bass. If you choose a beverage based on alcohol content and the ability to get drunk quickly, malt liquor is an excellent choice. If you prefer those attributes to things like taste and presentation, then malt liquor is an excellent choice. On the other hand, if you still want to get intoxicated, but maybe not as quickly, and want to savor the drink, a premium microbrew might be what you're looking for. The HD-650 will give you a flavorful experience - one you can enjoy rather than simply being hit over the head with one aspect.