First of all, V55 has 105dB sensitivity and HP700 has 100dB, so you will get some volume decrease with the same power. From my point of view, V55 runs perfectly without amplifier, while the HP700 can need it, depending on your listening levels, of course.
The huge improvement you will get is in the middle and upper frequencies, where HP700 excels. V55 has a very average midrange frequency response with a big deep around 1kHz., and an increase between 2 and 5 kHz. This sound signature makes some music very agresive and fun with for example electronica or rock, but its somehow coloured sound and metalic upper-mid can have a severe impact in acoustic or jazz. V55 can be also somehow boomy sometimes.
HP700 will give you an outstanding middle and treble frequency response. Voices sound natural, with texture and detailed, the phones are very musical and have a gorgeous soundstage for a closed can. The bad point if you come from V55 is that you won't find that enjoyable bass in there, specially because V55 has very fun behaviour in the subbass zone. HP700 can be mod to get more bass (I didn't try it), but in any case I have doubts regarding the subbass zone.
In my opinion I'm ready to sacrify the boom for getting into the real music (middles and harmonics), specially because bass can be a question of perception, and once is there (I mean it exists and HP700 do it down to 20Hz), your mind can always bring it up after a while. Other reason is that electronica or modern pop comes already with a big bump around 50Hz-60Hz. so no need of more bump there.
Regarding portable amplifiers, Fiio e6 or e11 will be more than enough for the HP700. Remember that both come with bass enhancer setting, so you can always compensate the bass of the HP700 if you don't want to mod them.