Different parenting styles - how strict is too strict?

My daughter (13) told me her mom makes her do chores with no screen time privileges, homework comes before literally everything, really strict rules. At my house we're more relaxed—she does her homework, but if she wants to unwind with TikTok after, that's fine. Now daughter's saying "you're more fun" and asking if she can live with me permanently. I don't want to bad mouth her mom but also... is her approach actually hurting our kid or am I just the cool dad and should shut up about it?