Our home has a well. It's ours - no well company owns it, never even heard of that to be honest. Two months after moving in some valve at the bottom broke (which means the pipe didn't stay filled, and thus unpumpable) and cost us like $300? to have someone come out and repair it. I could have done it myself, but I had no idea what was wrong or how to fix it - now I know /shrug You may have less water pressure than city water, too. We have a pretty small tank, for instance, so it's set at 32 psi, while local city water is at like 62-64? psi, so literally half the water pressure everyone else has. It's highly important - mandatory - that if you end up going with a place with a well that you get a full water test and well inspection. You or they will send a water sample to a lab and it'll tell you everything in there, how much, and give you nifty charts showing what it means. Likewise, the inspector will see how long it takes for the well to recharge (refill with water after being pumped) which is important, because if it's too slow..., as well as confirm well depth, water depth, and integrity of the hole itself.
On the plus side, you don't have to pay for water, though you do pay the extra electricity to run the pump. I like that the pump tells me if there are any leaks anywhere in the water system - the pump goes off when no one's using water. I found a leak outside that I'd likely not have even known about otherwise, so in a weird way it's a nice peace of mind kinda thing. On the minus side, I know that one day the pump motor and water tank are going to die, and that's going to cost a couple bucks to replace (hundreds for the tank, thousands for the motor).
Overall, if I could get this same property with or without a well, I'd likely choose city water, just so it's one less thing to have to deal with, even if cost-wise in the long term the well may be better (and I'm not convinced it is, who knows).