Which sub operation is more expensive in the AES encryption process?
The table lookup implementations usually combine the SubBytes and ShiftRows steps with the MixColumns step.
Different implementations/hardware/etc make general statements impossible, but this paper gives some  benchmarks and information on a table-lookup implementation.
It won't necessarily be quicker across all systems.  As per this paper:

It must be noted, anyway, that using a large amount
of memory for the look-up tables is too expensive for small systems, like for
instance smart cards, and is considered unsafe, as monitoring the accesses to the
look-up tables may in some cases allow to infer the key.

As an aside, another (better) way to speed up AES is to have the instructions built into the hardware