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.
Turn off wifi on both machines and connect them directly together with an ethernet cable. Then boot the new machine and during system setup it will ask if you want to import data from another Mac. Say yes and just follow the prompts. During that process it will tell you to launch Migration Assistant on the old Mac.
You don't need to turn on file sharing at all for this to work.