My mind is racing here, so bear with me-
I have never heard of a rental agreement that would make the renter responsible for the water heater or any plumbing for that matter.
The smell is just as likely coming from the well water and replacing the heater will do nothing to correct it. If you are in some twisted way responsible for the home's plumbing, you might want to have the well water tested to see if water treatment is recommended.
The main benefit to a new heater would be that a replacement heater may be a little bit more energy efficient. If the old heater lasts 5 more years it would not pay for the "upgrade". There is no difference between the 6/9/12 yr tanks except the warranty. The new water heaters on the market tend to last 1/2 as long and have twice the problems that the old heaters did.
Unless you would lose a great deal to damages if your existing tank springs a leak, I would leave it alone.