In my experience it doesn't.
The X3ii will put 224 mW into 16 ohms, 200 mW into 32 ohms, and 24 mW into 300 ohms
The E11K (or A3) will put 450 mW into 16 ohms, 270 mW into 32 ohms, and maybe about 30 mW into 300 ohms
Now before you talk about the extra power - lets see what that power will actually do. Unless you have extremely hard to drive (low sensitivity) headphones at 16 ohms, and even at 32 ohms, that extra power is wasted. In a real world example - go line-out from X3ii to E11K with a low impedance headphone or IEM and see how much of the pot is usable. Get my point?
I have the E11K and the X3ii. There is very little difference (if any) sonically between the X3ii line out and headphone out. I've checked volume matched - and I couldn't tell them apart in a blind test. I really doubt too many others would either.
The benefits of adding an amp to the X3ii are:
- Extending battery life (through not using the X3iis internal amp)
- Adding hardware EQ (bass boost), or in the case of the E17K I use - tone controls
If you're counting on sonic improvement past those two points, you're going to be disappointed.
However - if you're not volume matching, and not testing blind, and you want to believe that its adding some sonic magic - all that matters is what you think. If it gives you pleasure, then it is right