I have two different brands of induction burners and a gas cooktop (the latter one I don't really like and wish I had my old glass cooktop back from a former home).
I also own many different types of cookware...........non-induction-compatible stainless steel, induction-ready ceramic-coated, Le Creuset enameled cast iron, Induction-ready stainless and more.
I've found that certain types of stainless (depending on what type of bottoms they have) are very slow to heat up on the gas cooktop, and they make me miss my glass cooktop.
I've also found that certain induction-ready pans may work better or worse on the induction burners, again depending on unknown factors in how they are made and what they are made of.
It's a trial-and-error process figuring out which cookware works best. on which cooking surface. I'm still workin' on it!! But will say that the Le Creuset works best on everything.