This is one of the core features of SQLite.
Stable Cross-Platform Database File
The SQLite file format is cross-platform. A database file written on one machine can be copied to and used on a different machine with a different architecture. Big-endian or little-endian, 32-bit or 64-bit does not matter. All machines use the same file format. Furthermore, the developers have pledged to keep the file format stable and backwards compatible, so newer versions of SQLite can read and write older database files.
Most other SQL database engines require you to dump and restore the database when moving from one platform to another and often when upgrading to a newer version of the software.
http://sqlite.org/different.html
Check the code that's passing the databases. Do a byte-by-byte comparison to make sure they're equal after transfer. This definitely should be working.
Beyond Compare has good binary file comparison support.