I also have a range with an induction cooktop and convection oven. It's a Frigidaire, we got it when we remodeled the kitchen, ~5 years back.
I had several pans that worked, and several that didn't. The ones that don't work have been put in the attic and slowly donated to college kids (my own).
Mine heats water very, very fast. If you stick your finger in the pot, you can feel the heat increasing. OTOH, when you turn it down--the "power" setting spews like Vesuvius when it gets going--you have to go in stages a bit--if you turn it down to, say, 5, it'll stop boiling. So, you go from P to 8 to 6 to 4 to 2, over the space of a minute if, say, you're cooking spaghetti. I don't find this bothersome, but it's a quirk.
I find with the induction oven, I use the shortest cook time given. The only exception is cookies--I think it's because we use both racks for cookie sheets, so the air doesn't circulate as much. But, the cookies turn out fine. I haven't had any recipe that hasn't worked out fine, with the exception of operator error.
My top burners are different sizes, but they only heat up where a pan is on them, if that makes sense. They cool down very quickly if you take the pot off (longer if you leave it in place, which makes sense).
I don't much care for the digital thermostat, but I think I'm hosed there. It's probably a "me" problem--I have having to push the button a bunch of times (it defaults to 350--if you want 425, say, it goes up in 5 degree increments. It gets old!)
I'd be happy to answer any questions.