To use Migration Assistant / Target Disk Mode to migrate your 'older' Mac that has FireWire800 Port to a 'New' Mac that has no FireWire but instead has a Thunderbolt Port.
Using Apple’s Thunderbolt to FireWire Adapter
This does still work, but not the same way Migration Assistant works in Target Disk Mode with Firewire to Firewire connection.
The Tutorial below 'Transfer Mac (FW800) to new Mac (Thunderbolt)" explains how to use Migration Assistant to Transfer from Older Mac (FW800 to a New Mac (Thunderbolt) using 'Thunderbolt to FireWire Adaptor'.
To download the Tutorial
Click on the image below, it will open in a new window in Safari.
Go to File > ‘Save As’ and download the PDF to your desktop