Agreed with jja34-1 above that the Maybourne pool is larger and a bit more of a scene, and yes perhaps nicer. I really enjoyed the Peninsula pool - to me, it feels more charming/classic Beverly Hills, and the cabanas are great. In either case, you won't be missing out on a good pool experience, or, as you say, enjoy the sunshine and a bit of relaxing outside. In terms of location, yes with the Maybourne you walk right out onto a bustling street, and the Pen is a touch (a literal 3 min drive, or 12 minute walk) out of the mix.

It's likely not helpful, but my partner preferred the Maybourne (he enjoyed the energy and the cigar & whiskey bar), and I preferred the Peninsula (I love that rooftop terrace for lunch and the pool). FWIW, we also got upgraded at the Pen and didn't at the Maybourne, and the room always biases my experience lol. To echo the above, if you want something more refined and maybe quiet, the Pen; if you want something with a bit more of a scene, the Maybourne. I'd venture that whatever you decide, I think you'll have a good experience - and they're so close you can easily meander over to the other for a drink or a meal to check it out.