My dad built his house in 1961. Being in the hvac business, he had his men install a carrier oil furnace and 3 ton carrier condensing unit which used R-500 refrigerant ( a mix of R12 and R22 developed by Carrier).
In 2003 a natural gas line was installed on his street. At that time he installed a new gas furnace, coil, and 3 ton condensing unit after removing the still operational oil furnace and condensing unit from 61.
That said, I'd strongly disagree with the idea of keeping a system from the 80's on the theory that it'll be more reliable than a new system. In the mid 80's, a EER of 7 was common. Current base level units start with a minimum EER of 14. IOW, the current unit will deliver the same cooling while using half the electricity of the unit from the 80's.
The decision to keep or replace an old but functional system comes down to expected payback time. Most people have a month or so in the spring and fall when little heat or cooling is necessary. Comparing power bills from those periods to ones from the cooling season gives a fairly accurate estimate of your current cooling costs. If cutting those costs by half would recover the cost of a new system in 5 years or less, it's a pretty decent investment. The longer the payback period past 5 years, the less attractive replacement becomes.
In general, going to a system with higher EER will increase the length of the payback time, but that's also dependent on electric rates in the person's area. All done, someone in an area with a high cooling load and high power rates might have a 3 yr payback while the same system installed in a low cooling load and low electric rate area couldn't project payback in 10 years. The former should replace tomorrow if the money's there, but the latter would be smart to run what he's got until it croaks.