As per this wiki, you can ask your module exactly what version it is, e.g.:
>>> import sqlite
>>> sqlite.version
'1.0.1'
>>> sqlite._sqlite.sqlite_version()
'2.8.16'
So what versions numbers do you see when you try this?
A list of release note links from pysqlite version 2.3.4 to 2.5.5 (about 2 years' worth of releases) is available here -- so if you were using the 2.3.2 embedded in the sqlite3 that comes with Python 2.5 or the 2.4.1 that comes with Python 2.6 you could trace exactly what features, optimizations and bug fixes you might be missing (a long list). But 1.0.1 is SO far back that I don't know where to find a further list of changes from there to 2.3.2! Looks like a job for an archeologist...;-).
I've seen a pysqlite tutorial here; full docs (LaTex sources) here; good luck!