ReeReeIncorperated

I'll clarify this for OP since this requires context.

PS Plus Premium (the highest tier, there are two lower tiers) is roughly $20 less than Gamepass Ultimate. So it is slightly cheaper.

PS+ Premium has two catalogs of games: The Modern Catalog (PS4 onward) and The Classic Catalog (PS3 and before). From what I understand, the Modern Catalog has up to 503 games in there, and the Classic Catalog has 446 retro games. (Via IGN). The classic catalog's PS3 titles, which I believe is most of the catalog, require game streaming. It isn't that good of streaming, and I have ethernet, so unless you have godtier internet, good luck. The modern catalog and the rest of the classic catalog do not require streaming of any sort.

The Modern Catalog has a lot of games, but they're not all that fire. It's a lot of fluff and not as much heat as I'd prefer for an almost $200 subscription. The games in the catalog are also not too new, so don't expect many games that aren't from at least 1 year ago. For the sake of OP's kids, there also isn't a good selection of games for the young ones. This doesn't impact the quality of the service at all, but if you're buying for the kids, this might help define your choice.

Gamepass Ultimate has 480 games in the service from each generation of Xbox. This includes all titles in EA Play, which is basically every EA game except for the dead ones. In contrast to PS Premium, Ultimate's game selection is much higher quality. There is a lot of fire on this service. Furthermore, Xbox has constant day-one releases dropping on gamepass, including every one of their own titles, so you won't be playing as many classics as you would with PS+. Due to the nature of there being a lot of heat present, heat also leaves every month, so you might get occupied with one game and miss out on another one you want to play. And for the little ones, there is plenty of kid games on the service, so they got their content.

Gamepass Ultimate also gives you access to the service on any platform it is available on, which includes consoles, PC, and Xcloud. Xcloud is a surprisingly smooth and stable streaming option for games that I even occasionally use. Because of this, Gamepass is super accessible and you don't even need a console for it, though I'd still recommend buying one for a gamepass machine. Another benefit, albeit very niche and you might not use it, is the Gamepass Quests for Microsoft Rewards. When you complete quests, you get Rewards points, which can lead to you getting free store credit or gamepass. It exists.

Overall, both are valid options. If you want a more quantitative selection of games, go PS+ Premium. If you want a more qualitative selection of games, go Gamepass Ultimate.

Gamepass.

You want to keep your kids occupied with games without having to spend much throughout the year? Gamepass. Hell, it'll keep you occupied as well