I don't like 3-speeds much. The gaps are just too big to keep the legs humming along nicely during dedicated riding. Its more like a 3-in-1 bike than a geared bike.
It can be OK for casual/utility riding though if you get the basic gearing ratio set up right.
To me, 5-speeds (and above) is where it gets good.
Performance is endlessly debated.
External gears have smaller losses under ideal conditions.
IGH setups are generally heavier.
Removing the wheel takes longer.
I've never seen a comprehensive study on efficiency during real-life riding. But I'm convinced the difference would be smaller.
As long as I have the range&ratios I want, I'll ride either.