Can I use Titanium Backup to migrate from a Galaxy S2 with custom rom to a new Sony Z1 Compact? Next weekend I plan to buy a Sony Z1 Compact. Right now I have a rooted SGS2 with Android 4.3, custom rom (Avatarrom). I use Titanium Backup and this has always been great for restoring apps including their data, but that was always on the same phone. I think I'm going to root the phone immediately, connect my google account, reinstall all necessary apps from the Playstore, and then use Titanium backup to restore data only. I'm not going to install a custom rom right now I think. 

I wonder if this is going to work out, if you have tips, what the risks are, what to watch out for.
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.