Yes that's important too, but the magnitude of difference is relevant.

A local shell with a non-pathological shell config and a reasonable terminal emulator is snappy-ish.

Most sluggishness can be fixed in shell config. If that isn't working, some terminal emulators are definitely faster than others, especially on Linux with its wide variety of modern and historical choices! And of course tty will always be faster still, but far less convenient.

When all is said and done and properly optimized, it's all probably still slower than the ProDOS prompt on an Apple //e (1MHz 6502 CPU), which can't help but make you wonder what we've all been doing for the last 40 years!