I worked in a restaurant, loved the responsiveness of gas, and was dead set on replacing the old coil stove in my house with gas. But after some research, I took the leap on induction and was blown away.
A full kettle starts boiling in like two minutes tops. No residual heat sweating up the kitchen. I can even shut the element off right before taking the lid off the pot and I don't get blasted with steam. It's more responsive than gas, more consistent, and I don't need crazy ventilation. And cleanup is as simple as it could possibly be, I can even just lift up the pan and give a quick wipe during cooking because the cooking surface itself doesn't actually get hot (except from the heat of the pan, but that's negligible for a quick wipe).
I think the only reason your SIL insists on gas is because she's never actually used induction, or maybe she's just a weird luddite. As a long time gas-supremacist, induction is just better all around.