Does he want to play online, with his friends? If so, he will need whichever his friends have. There are very few games where X-box and PS gamers can play together.
Call of Duty is available on both, but Microsoft have just purchased the developers, so in a few years, once existing contracts have been fulfilled, future CoD games will probably be only on X-box.
If you are on a budget and don't want to spend a lot on games, then consider an X-box with Gamepass. That is a service like Netflix. It has all Microsoft-owned software on it (unless the licence has run out) and a lot of third party games too.
The options at the moment are:
PS5 disk version.
PS5 digital edition.
X-box Series X
X-box Series S
The PlayStation disk version is more expensive, but the games are a bit cheaper, and it allows you to buy second-hand games (as well as games from the online store). The PlayStation digital edition is cheaper, but then your only option for buying games is from the online store, which is expensive.
X-box Series X is for disks and games from the online store, and is the most powerful of the consoles. That said, the difference in performance between it and the PS5 is usually not very noticeable. X-box Series S is slightly less powerful, does not take disks but is a fantastic bargain, especially with Gamepass. It is also the one that's easiest to find - the PS5 in particular is very difficult to get hold of.
I prefer the X-box for its driving games, although PS5 has a flagship driving game coming out soon (Gran Turismo 7 in a month).
If he's the one who's going to be using it most, I'd recommend that you ask him which one he'd prefer. If the PlayStation he used to have was a PS4, then games for that will work on the PS5 (with about eight exceptions). Likewise games from the last X-box will work on the X-box Series.
The RRP of X-box series X is 450 pounds in the UK. Series S is 250. PS5 is 450 for disk edition and 360 for digital.
Or you could get a last-gen console more cheaply - PS4 or X-box One. The most recent of those is PS4 Pro and X-box One X.