Well, why are we doing a 20/100 split anyways? It's more likely there's a mid/standard tier in the 40-60 range that will end up his best choice. 80-120 is always premium tier and probably not needed for his usage.
If your Verizon option is FiOS, get it and don't think twice. If it's DSL, then you probably want to do some research/googling into how the two ISPs fare in your local area. For density, you just need to ballpark it; deep suburb, lower Allston apartments, midtown Chicago, etc.
When you do get set up, a thing to do is plug something wired directly into the modem (altho it sounds like you'll need to use the PS4 for this) and go to any number of browser websites (
speedtest.net) to set a benchmark ceiling for your top speed. Do it at peak time, like Thursday 8PM. That will both give you a sense of how close the ISP comes to meeting the advertised speed, and be a useful point of comparison for any downstream troubleshooting you have to do later on.
Edit: Also, doesn't Cox have pretty shitty data cap policies? That could be a dealbreaker; make sure you check out that part of the package.