The purpose of an uninterruptable power supply (UPS) is to continue to supply power to mission critical devices after the power company's power fails completely, or goes too low or too high in voltage. Your "battery backup" is a UPS. The power is provided from a battery that is charged while the power from the power company is OK. How long the UPS will continue to provide power after the power fails is a function of the battery size and the load imposed by the connected equipment. There are three common types of UPS: standby, line interactive, and double conversion. A standby UPS switches to battery power when the power company's power fails or the voltage goes too high or low. A line interactive UPS does the same, but also adjusts for low and high voltages within limits while the load is running on power company power. You can get the same voltage regulation in a device that is not a UPS. You really don't need it in either case because the power supplies in your gear are designed to work properly across a range of input voltages. A dual conversion UPS is analogous to always running on battery, pretty much separating your gear from typical power quality problems like sag, harmonics, etc. This is generally not a problem for AV gear. The power supplies usually handle these things just fine.
The question you have to answer for yourself is what is mission critical. A lot of folks think that keeping a projector from shutting down without a cool down cycle is important to keep the bulb from being damaged. It isn't. The bulb is actually happier cooling down slowly. The cool down cycle is there for other reasons. Some people think their DVR is mission critical. They cannot stand to miss an episode of their favorite program. This makes more sense to me. Some people put their AVR on a UPS. Makes absolutely no sense to me in most cases.
UPSs typically provide some degree of surge protection. But that is not a reason to buy a UPS.