So, a benchmark.
[email protected]:~$ time zsh -i -c exit real 0m0.064s user 0m0.048s sys 0m0.008s
[email protected]:~$ time bash -i -c exit exit real 0m0.540s user 0m0.436s sys 0m0.100s
Both shells had their respective completion systems enabled. (Without them turned on, bash actually beats zsh... but the times are small enough that it doesn't matter.) These times are with a warm disk cache - the first time through both shells were slower. And the numbers stay roughly the same when repeating.