Have a listen with / without the amp when you get time. Keep testing both with, without, with without, Tell me if you think some of the treble, clarity and detail is lost using E11. Don't worry about which one goes louder, forget about all that, use an average volume, see if you can pick out how much E11 colours the signal with loss of clarity in the mids.
I find it's quite a lot and I'm willing to go without.
Ok. will definitely spend a whole a lot of time with and without this set-up. Will let you know. Although, my current set-up is the iPod Classic + E11. It sounds a bit beter. But with the iPhone 4S +E11, I can't tell wether there's a difference without the E11.