[falcolas]

You listen to them. Listen to a piece of music that you know well, and listen to the two side by side. Ideally something which isn't all in one frequency range.

With better headphones, you will hear more detail in the sound. Words which sounded mushed together in the Beats will be distinct in better headphones. The mids and highs will come through much more clearly. Music will just sound better.

Beats have decent bass, but they're hardly the only ones with good bass out there, and many which have good bass are also capable of sounding better in the rest of the frequencies as well.

[superuser2]

This is an easy thing to say, but stores with a reasonable selection of headphones you can listen to are rare. The best option for your taste/budget at the Best Buy display, for example, are rarely the best choice for the money.

Many of the beast headphones aren't consumer products and aren't sold in mainstream retail outlets. I love my Sennheiser HD380s but I know about them because I'm an amateur engineer and they're great for live monitoring.

Really, just look at Sennheiser, AT, Shure, Koss, Grado, Beyerdynamic, ... Anything mainstream that's not Beats or Bose is probably worth looking into.