Having compared the E11 to my E7, without bass boost on, I can say this:
E11: Detail is more forward and I felt like I could drive my IEMs to ear shattering levels, this could be just because of the analog volume pot. It's sound signature seemed to be brighter than the E7. It's also thinner than the E7 (in size)
E7: As a DAC, it's not the most detailed I've heard, but definitely a big improvement over most on-board sound cards. It tends to be warmer sounding than the E11 with slightly less bass roll-off, yet a slightly bigger mid-bass hump. The digital volume control is very slight in adjustment which means I find myself clicking it several times to get to the volume I want. I usually listen at around 25 (limit is 60) so it has some room, just that it's not as convenient as a conventional volume knob. Don't know about the battery life on the E11, but the E7 will last for weeks literally depending on how much you use it at a time.
So, as a portable amp, I like the E11 better because of it's size and volume knob. A gain switch is also handy if you find that your DT1350s are hard to drive. If you want a DAC as well, and want more features (such as sleep timer, volume limit, higher bass boost, OLED display) then get the E7.
Note, these are my first impressions of the E11 vs my E7, so YMMV.
