The A xx services go directly to the airport. The seats are also
wider and the leg spaces are larger. Hence they are more
expensive.
The E xx services go to the various parts of the airport, including
the passenger building, catering centre, cargo centre, maintenance
centre, Expo, Tung Chung town centre etc etc etc before going
towards the city. The E xx services are for the locals, so it's
cheaper.
Normally tourists will prefer the A xx services because it's more
direct and more comfortable. But locals will prefer the E xx
services because it's much cheaper. For me, I live in HK Island and
I have a choice of A11 or E11. I prefer the E11 because E11 costs
only $22 but A11 costs $40. (I would rather spend an additional 15
to 20 minutes "touring around" the whole airport and save half the
cost.)