Thanks for the info. I should have made sure to mention that I won't normally be using them with my phone, it was just the only source available to test with due to the epic failure of the Guitar Center guy to operate his display equipment and I figured at the very least I'd get some idea of the Beyer sound and differences between a couple of their models. The easier drivability in general including portable amps is something that does seem to be a big plus for sure though and it sounds like for example those two Schiit products I mentioned would not really be a good match for the 600 ohm version. The Vali only has a 6.5 ohm output impedance which would mean a really high damping factor and even more on the Magni.
The damping factor you want is at least 1:8. If you have more it doesn't matter - you just don't want (rule of thumb) less.
The thing to be aware of is that the DT880 600ohm requires higher voltage rather than current. They are not low sensitivity but they are high impedance. This is why OTL tube amps with high voltage output seem to suit higher impedance cans.
When you get something like an AKG K701 (low to average impedance - 62ohm - but also low sensitivity), they require higher current rather than voltage.
Anyway - the Vali (hybrid) and Magni (SS) would probably drive the 600ohm OK - but if you were aiming for those as your amps - I'd personally stick with the 250 ohm.