The 600s seem different in that first you need to be able to drive them, so you get an amp, and they respond to the amp's characteristics more. But I'm no expert with these at all -- I've only had mine a few weeks. Perhaps the 250s show differences in amps just as much.
I'm able to drive my 600s pretty well with my existing equipment, but I'm looking for some character from a tube amp and these seem to be the headphones to do it with.
I can safely say this though, if you're getting enough volume now, a $50 amp isn't going to make much difference for you.