Fiio themselves have stated it.
The E7 uses the same amp portion as the E5, with beter opamps. The E11 uses a much stronger amp, and Fiio's rep James has stated that the amp also sounds better than the E7's internal amp. The reason it's cheaper is because it's a portable amp ONLY, as opposed to the E7 being a DAC and AMP. Just look up the E11 thread here in the portable amp section.
http://www.head-fi.org/forum/thread/527342/e11-a-new-start-of-fiio-s-portable-amp
1, Replaceable battery ( compatible with NOKIA BL-5B)
2, working voltage: +/- 4.5V or +/- 6V;
3, Voltage Gain: 10 dB;
4, Volume control: Alps potentionmeter;
5, OP: AD8397;
6, Output power: >150mW;
7, Case: Aluminium alloy
8, Playtime: 10 Hours
9, ETA: March, 2011
Edited by Mad Lust Envy - 3/1/11 at 8:51am