I am replacing a 27 year-old central ac system. Since it's a rental, I'm wanting something basic. A recommendation has been the 13 seer system from Payne, purportedly pretty much the same as a basic Carrier model. However, it does not have a hi/low pressure switch. How important is that switch? Is it worth paying a few hundred more for a basic Carrier model (24ABB3)instead?

The high and low cutoff safety switches can play an important role in protecting the unit. If for some reason the unit runs out of refrigerant the low pressure cutoff will prevent the compressor from running possibly drawing in air and moisture into the system causing damage.

The high pressure safety shuts down the unit if the condenser fan(outside fan) fails to operate. This can also cause compressor damage and it will prevent the compressor from going off on the internal electrical overload or is some cases preventing the compressor from activating the compressor internal refrigerant bypass.

There are other reasons for these devices but I will say that many units do not come with them from the factory. They can be added to the more reasonable price units so you might get a price on having that done.