Lithium - four 100Ah Dragonfly LFP batteries with their built-in BMS, and the Victron MultiPlus charger/3000 watt inverter. And we ran 20 amp 120 throughout so that we could plug in a cooktop inside or out. 640 watts of solar. Power is rarely an issue, though in the winter it's still iffy. Right now, we're parked in the shade and the panels are covered in snow, and it's 7° so no charging will be happening today. In these conditions, we just don't use the inverter and the batteries will last for days.
Down at Big Bend a few weeks ago we had sunny skies, and even then we would just barely recoup our power use when we used the toaster oven the night before - similar power draw to an induction. That's one of the reasons why we went with a propane cooktop. If we could tilt our panels, that would make a huge difference. I have a 200w portable, but I haven't wired for it yet, and I think that will make a big difference as well.
So we have the option to add an induction cooktop but right now we're pleased with LP. It's cheap, lasts for weeks and in the US can be found anywhere. Once we exhaust the US and Canada and head down south, we'll probably want to rethink things. But by then we'll probably be looking to swap out for something like an Earthroamer or Tiger anyway. That's a ways off and by then everything solar and battery will be quite different I'm sure.