SQLite3 has very few types, you cannot create new types, and is duck-typed.
PG has many built-in types, you can create new types, and is (mostly) statically typed.
You really have to know this going in. If you have to support both, you'll probably have to write two versions of your SQL -- or you'll end up using an ORM that supports the two RDBMSes, and then you may get stuck with the ORM.
SQLite3 is amazing, but it's mainly amazing because of how easy it is to embed in apps. If that's what you need, use SQLite3. If you need more power, if you're building a server, then think long and hard about why not just go straight to PG.
EDIT: SQLite3 is amazing for other reasons too.