You can tell if a fish has been flapping around on the deck - the muscles have been burning up, so the flesh is not as clear, you can see the blood in it and it doesn't taste as good. When you immediately use a spike to the brain, the fish stays still and the meat is better quality.
It is best to fillet it straight away in a clean environment, then chill it and let it rest for a day or two. That way you get the full flavour of the meat. There's many ways to eat bluefin. My favourite is as sashimi with fresh soy sauce and fresh wasabi, and I like to keep the cheeks and sear them for my breakfast!