My thoughts.
The real goal here is to spend a few of the last years you have with your son at home, bonding. With two college kids at home and both having eyes on that day when they move out of the nest, I get this in a big way.
Having said that, what is most important is how your son views this project. As long as he is satisfied with the version of "together" that you choose everything is good. To me this is less about learning an instrument than it is about creating an additional bonding point with your kid.
So, Bass or guitar? Having your kid's input would be nice, but remember if he brought this up then he probably has a picture in his mind of how this should play out. You can talk to him about it, but present it in a neutral way so that he feels really free to choose.
If your heart is with the bass but you choose guitar for some of the reasons above, your guitar time will not be wasted. Theory, rhythms, and the listening skill you develop will be more or less a direct translation when you eventually move to the bass in say 3-5 years.
Guitar or bass, each has a clear path to jamming together. Two guitars can play together just fine, trading eights, exploring harmonies, counter point rhythms etc, are all great fun. Bass and guitar are obviously great together. I would say reflect a bit and decide what you really want to achieve here.