We have the Rigid 12" 18V chainsaw. It cuts hardwood, pretty well up to 10". Not super fast, but it beats the handsaw by a lot! All chains need to be sharp which helps any saw. I've bucked up some 18" ash with it, and gets through that as well, without any issues, other than speed.
I register all our Rigid stuff for the lifetime warranty and rarely need to use it, but they did replace my ni-cads when they died, with L-ion batteries and a charger. I would just start buying rigid and gradually replace the ryobi stuff as it dies.
If you've got big trees, like 20"+ diameter, and expect to cut a few of them into chunks you can move after a big storm, then you need a good $1000+ electric with another battery or two, or a stihl/husky 55-60cc+ model.
If you are just buzzing up a fallen branch or two, even up to 16", then something like the Rigid can do that for a $2-300.