I own my tanks, and I fact have my original tanks from the 1970's, in addition to an additional five I've picked up over time.
The primary advantage to owning your tanks is convenience. You can dive on the spur of the moment, and do not need to rush out to the dive shop to rent and return tanks.
The primary disadvantage is the "cost of ownership"... you'll need to buy the tanks (expensive initial investment), and pay for annual visual inspection and periodic (every 5 years) hydro-testing. The good news is it should be a one-time purchase, since tanks will last forever as long as you take minimal care of them.
Where I live, the cost difference between a tank fill and a rental is only $2. So it takes a lot of dives per year to come out ahead financially by owning my own tanks.
But, the ability to go diving on a moment's notice is well worth it for me, and I'm very glad I own my tanks.
Also, I service my own regulators, and having clean compressed air at 3,000 psi to test them is a must...
Best wishes.