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:
Option 1:
Do a migration from old to new version.
Option 2:
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.
Option 3:
- 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.