Can I use Titanium Backup to migrate from a Galaxy S2 with custom rom to a new Sony Z1 Compact?
Be careful with restoring data from system apps, that might break things (and you'll have to factory-reset and start over). Different ROMs, different (structures of) system apps (their databases might differ). I had that once; in my case, affected apps (e.g. SMS) simply force-closed either right at start or shortly thereafter.

If you really want/need to restore system data, make sure to enable TiBu's "migration mode" (in the settings "troubleshoot" section). That way TiBu won't simply replace the apps' databases, but only try to "merge in" the data.