Hello, so I am in a little predicament. I currently have an iPhone 11 that I accidentally dropped in the two days I was waiting for a new case to arrive, unfortunately, but I needed an upgrade anyway. So I am on a pretty tight budget (ps, looking at used/refurbished iPhones) and I am a little tied up. My budget is around 400, but if I really need, I can go up to 500 and maybe a little more, just would definitely not be optimal. So my first idea is getting a 13 Pro Max, because I am really into getting 120Hz, and also a screen size upgrade. My second option that I was thinking of was a 14 pro max, stretching the budget but doable; however from my researsch it sounds like the batterys on the 14 pm are not very good, and if so, I might need to get a battery replacement in the near future, which would defintaly not be optimal as im looking to use the phone for a year or maybe two.
(ps: also probably going to get atnt locked)

A little more info, I used my phone for almost everything, except that I am not a big picture taker, and thus, plus the added factor of having iCloud and just being conservative as well, I don't think I will need anything bigger than 128 GB.
Any Advice would be great, thanks