Reduced to a strictly economic decision, I suspect that most recreational divers will find that renting is cheaper in the long run than owning. Nonetheless, I know that I found it more convenient and safer to own my tanks, if not always the most cost effective decision...
Owning your tanks means never having to call the dive shop to see if tanks are available. If you own your tanks, you can get fills on Tuesday morning if that's the most convenient time for you. It also means that you only need to make one trip to the shop - for fills - instead of two to pick up and then drop off the tanks.
Owning your own tanks also means that you know where they've been and how they've been treated. Anyone who inspects tanks has some pretty frightening horror stories about some of the things they've seen inside some cylinders. Nobody treats rental gear with extra care, if you own your own you breathe easier, figuratively and often literally.