When I travel, for instance to cook for the inlaws on holidays, I have to spend time physically correlating how hot each of the burners is for its particular settings. It seems to vary between each individual burner, which are different sizes. The way I correlate is to use my bare fingers to quickly touch the bottom of the pan. Or I lift the pan up and touch the bottom there. This seems suboptimal. When I travel to AirBnBs, induction ranges are all the rage. Same process. I suppose if you're boiling a pot of water, the induction speed is great. If you're making something sensitive like a hollaindaise, lordy what a PITA, in my experience.
I make delicate sauces like hollaindaise reliably and speedily on my nominal 15,000 BTU gas range. I have had the family twiddling fingers more than once waiting on me to get results from an induction burner. Same burner is an outstanding large volume frier.
Now I get that the induction technology is safer, but then I use a big chainsaw with a real chain to cut down trees on my property. Chainsaws are highly dangerous and exceptionally useful. Similarly I raised up a child that learned to cook quite sophisticated things on that big gas range. She was also using very sharp 12" knives from an early age. There can be a deep pleasure in "be here now", paying attention to your tools, using them competently and safely.
(It's possible I've only ever encountered crappy induction cooktops...)
Again, I don't know the safety characteristics of induction so maybe I did something really stupid...
I believe higher-end stoves will either not pulse or pulse fast enough to effectively be continuous when you factor in the thermal inertia of the pot.
Gas stoves are the next most responsive because the fire doesn't "store" heat; only the grill does.
Finally electric stoves are the slowest-responding because the coil stores quite a bit of heat even after power is cut, and that heat continues to transfer into the pot. Conversely, when starting them up, it takes quite a while to heat up the element hot enough to only then transfer some of that heat into the pot.
You do want a quality induction stove with an analog knob for the best experience, though. The low-end induction stoves typically have touch-step controls and pulsating simmer, which IMO is still way better than an electric stove if you're on a budget, and still responds faster than gas stoves but lacks the fine-grained simmer controls that some of the higher-end models do, if that is important to you.