If you're running into concurrency issues, than both MySQL or Postgres are good solutions. Tanks compared to SQLite? Yes. Slower? No.

But if you're looking into something small, check out Firebird (http://firebirdsql.org/).

It's fully ACID compliant relational database, can work both in embedded or client/server mode, fast, easy to maintain and cross platform. IMHO, the only drawback of that RDBMS is small(er) developer mindshare. I worked a lot with it before (8 years ago) and loved it.