If I have to choose between PostgreSQL and FireBird, it's not a question: unambiguously PostgreSQL. But it's only my opinion... :)
Anyway, we are using PostgreSQL in enterprise environment since years, and we are really satisfied with it.
Do you use JPA ?
If so, then what do you mean by feature limitations or size limitations?
Are you willing to use database-specific, non Standard-SQL or JPA-conform syntax
with the cost of database-vendor-dependency?
It is good to know, that Projects with JPA can be swapped to databases no matter which vendor.
Which tools do you use with Postgres for managament/current sql tracking etc... in production?
I think mysql has a much more usable tools than postgres for management purposes.
Otherwise choosing between mysql and postgres. I vote postgres too.
Postgresql because i doubt that if mysql haven't sufficient feautures for your application, firebird could have more feautures then mysql.