Neon optimizes it's storage architecture to make any point-in-time lookup of pages cheap, whereas Aurora only maintains the latest version of a page. This means that Neon only stores the differences between split branches, while Aurora stores a whole copy of the data - or at least, that's what you pay for.

Other changes are that Neon still (mostly) uses Postgres' XLog storage format, whereas Aurora does not, and that the source code for Neon's storage engine is fully open source and supports PostgreSQL 15, while Aurora is closed-source and doesn't.