The only surprise I had was that they don't show you any database logs! Turns out I haven't needed this so it's not a big deal, but that's the biggest departure from a "traditional hosted postgres" service.
Aside from that, the only missing feature is the ability to create an Organization rather than hosting projects in a personally-affiliated account, but this is apparently coming soon.
The branching features work really well and I've used it a few times now to debug issues and test migrations without impacting production. I haven't set up the per-pull-request-preview-environment stuff yet but I plan to and I like that Neon makes it easy.
EDIT: oh, the one other annoyance is that last time I checked, it was not possible to create a read-only replica in a different region than the primary compute node. Or something like that, I'm still not sure, and multi-region read replicas are not particularly necessary for me right now (Devlog still in early alpha, not a lot of customers) so I just moved on. Issue tracked here https://github.com/neondatabase/neon/issues/4178