I haven't heard the LCD-2, but it's supposed to sound very different than the HD 700. The LCD-2 has a more dark sound - tilted downwards with more bass presence, warm mids, and subdued treble. That's what people say anyway, and I have heard the LCD-3 which is the LCD-2's superior by most accounts, and I can say that those adjectives apply to the LCD-3.
The HD 700 is a more neutral sounding headphone with some warmth in the mids. The thing that people dislike about it is the treble, which has sibilance and some find it to be too powerful (not me). The HiFiMan HE-500 is significantly less costly than the HD 700, and also better in pretty much every way. This isn't just my opinion but I'd wager 99% of Head-Fi agrees. I don't think the HD 700 is bad but the HE-500 is just the more transparent headphone, both are geared towards neutral sound but the HE-500 doesn't have the treble problems that the HD 700 has.
Another headphone in that price range is the HiFiMan HE-560, which like the HE-500 is a mostly neutral headphone but with stronger treble, more detail, more airy sound, better sound stage.
Although this thread is full of subjective impressions, it might help you get an idea about the differences between these headphones and others.
http://www.head-fi.org/t/634201/battle-of-the-flagships-58-headphones-compared-update-audeze-lcd-2-revision-2-6-4-13
But since you liked the LCD-2 so much, that's already a safe choice. I really don't know squat about portable amps.