I own the Beats by Dre, HD 650's and HD 595's.
The HD 595's are the closer in price to the Beats by Dre, so I'll start with that. Compared to the beats, the audio just sounds thin in comparison. The lows are nearly non existant (until you get an amp), the mids are slightly better, but the highs also lack in comparison. The only thing I love about the 595's are the soundstage.
Now...The HD 650's. These are better than the Beats by Dre any day IF and only IF you use an amp with it. The 650's sound barely better than iPod headphones without an amp (ok, maybe that's an exaggeration, but they sound horrible). With an amp, the Beats by Dre aren't even close to the sound quality of the 650's.
Bottom line is that unless you're only going to be listening at home, the Beats by Dre are excellent. They don't need, nor benefit much from an amp. They are great for wearing publically, as they don't look like the other gigantic, audiophile headphones out there. And so, your music won't sound like absolutely crap coming out of an iPod.
Most "audiophiles" claim that the Beats are absolutely useless. Yet, they are either going by word of mouth of their other, misinformed buddies, or haven't given them a good listen. Listening to it at the Apple Store isn't a thorough listen. Audiophiles will want to take any other pair of cans home, plug it into their audio equipment (dac, amp, etc.), let them "break in", and then give their opinion. But for some reason, with the Beats, this basic etiquette doesn't apply and many believe that because the notorious Monster Cable is branded on there, they won't sound nearly as good as other $300 headphones. Wrong.