The pump was less than $200 and I had a friend of a friend install it for about $100. If there's a water line close to your sump, it's not really too tricky to install.
A battery requires a homeowner to check its status, and in an extended flooding situation, will eventually run out.
A water-powered system will always work. Unless there's a problem with the float.
I think it cost about $200, and we installed it ourselves. Bought it at Home Depot.
Power was out for about 6 hours while we were away. My neighbor got at least 6 inches of water, and my basement was dry.
Lots of the cost is in the battery. I think a replacement battery costs close to $100 plus another $20 for the acid pack. Batteries have to be replaced every few years.
It's an afternoon project. Guy at the HD just threw all the parts I needed into the cart. Replace the battery every 3-4 years. Probably a good idea to keep a spare as well. We had a massive storm here where we lost power for 16h and burned out the battery. The battery shelves at the hardware stores were bare the next day.