My understanding is the lots of small cores are for applications where you have lots of simple, independent tasks that tend to be IO-bound: web and other front-end servers, databases, transaction processing. SMT is optimal here because you can execute other threads while waiting for IO.

I haven't been closely following it, but the Intel E-cores are definitely less wide and have less execution units. The FPU/Vector hardware is 128-bits wide instead of 256. If you ask it to do 256-bit SIMD, the front-end breaks it into 2 operations.