DT770 has stronger and deeper bass and good highs, but recessed mids. Consider it the V-style equalised cans, the equalizer shape you probapy see in lots of car amps: boosted bass and highs, leaving mids down. If you get DT770 Pro, 80 ohm model, it should work without extra amplification decently, but some extra amplification is recommended. Portable amps are not bigger than pack of cigars, not much bigger than ipod itself actually, so its not a burden to have one.
Havent heard A900 personally, but from what I have read, it has slightly more balanced sound overall compared to DT770. There is a dip in lower midrange that might give it slight nasal color to sound, and bass is very slightly boosted. Simply put, not as heavy sounding as DT770 or so they say. Works really well without extra power, very efficient cans.