The new one has no Firewire 800, the old one has no Thunderbolt. Short of spending quite a bit of money on a Thunderbolt to Firewire 800 adapter and a Firewire 800 cable you're going to use once for Target Disk Mode, I'd use Ethernet.
Connect an Ethernet cable between both systems.
Enable the File Sharing on both systems.
Add your boot drive to the shared list on your old Mac.
Boot them both. Your old Mac will show up on the desktop as a network drive.
Use Migration Assistant to move your old user data and files from the old Mac via the shared drive.