From a safety standpoint, induction is the clear winner. Induction stoves shut off when they overheat or when they run longer than 2 hours. They can also keep a present temperature.
But the downside is you'll need compatible cookware, which can be expensive.
Aluminium moka pots aren't. Copper bottomed pots usually aren't. Woks don't really work without a flame. Bain-maries that work on induction tops are about 50:50.
The only thing I miss from gas is my wok. All other cooking on induction is superior. Definitely worth sacrificing a few old pots for. I would love a good wok solution though.
Bialetti makes excellent moka pots for induction. I find it even better on induction stove to control the flow as you can basically leave it on "5" and coffee slowly pours out. Much harder with real fire.
When my wife and I first started dating I bought her a bunch of expensive stainless steel cookware from a restaurant supply store, that we still have. I recently pondered switching to induction, and went around doing the 'magnet' test on things, only to find that those pots and pans are likely not induction compatible.
So the conundrum is... toss the pans I gave my wife over 20 years ago? Or just stick with electric burners.
Try one of those inexpensive induction burners first. I was excited to try them because of the promises you hear about how much better they are, but once I got one, I quickly grew to hate it for everything except boiling water. The temperature control wasn't fine enough. There were only 12 temperature options and there were big jumps between them. The first temp is 140F and the next is 212F. No simmering, in other words.
If you like to cook (and I'm assuming you do, considering that you bought expensive cookware), I would definitely recommend auditioning an induction burner before you go through the expense and hassle of switching out your stove.
According to my research, there's only one burner that is very expensive that works with US power levels that allows you to move in 5F degree increments and uses a thermometer for feedback.
Most of the ones you are referring to are European models that work on 240V. If you know of one that works on 120V, please point me in that direction.
I apologize, I didn't take 120V constraint into account. But even in EU, the cheaper induction stoves are significantly worse than the midrange if one is even slightly interested in cooking.
The initial cost isn't higher if you are buying new pans. New, cheap pans usually work for an induction stove.
But you might not have new pans, nor the money to replace all of them. Especially if you rent and have no control over what stove gets installed when your current one breaks - or just move into somewhere to discover the induction stove. It is kind of like buying toilet paper: It doesn't matter if the 24 pack is cheaper if you only have the money for the 4pack. Running costs don't always matter if you don't have money to invest upfront.
And to be fair, they aren't inserts. They sit between your stove and the cookware. The plate heats up and heats up your cookware, much like your pans heat up to cook your food. It might take slightly longer, but it won't realistically be worse than heating up a cast iron skillet. And you have a stovetop you can use.
But the downside is you'll need compatible cookware, which can be expensive.