I'd have a go at migrating, but it may be easier if the old and new sites are on the same version of Trac. I'd probably go about it this way:
Consult the software site for upgrade info - especially about database versions - and see if this gives any clues. Based on what I discover:
Do a migration from old to new version.
Install the older software (if available) on the new box, copy over the database, check everything's working and then try the upgrade on the copy.
- Clone the current server to a spare box
- Upgrade the software on the spare box to the latest version and see how the database fares
- Decide whether it looks likely that the database can be taken over onto the new server
As a last resort, I'd backup all files and data from the old server before trying an upgrade on it - but I'd really have to rule out the other two procedures first.
Hopefully, one way or another, you'll either end up with a working, upgraded install where you want it or you will have a working install that can be copied/migrated.