The biggest advantage is cleanliness, and this mainly not while riding, but in handling the tandem.

I have two tandems, one with a Gates, and one with a chain. The sync chain on a tandem is very long and prominent, and handling a tandem is awkward enough anyway that it is a threat to get grease all over anything it gets near. As a result, a tandem with a sync chain is a low grade menace, like a wet dog at a wedding reception.

A tandem with a belt is a different animal. You don't mind getting and keeping it close. Into the car? Into the house? The hotel room? No problem.

With riding, I am not sure there is much difference. The weight advantage is overstated, it isn't that much (I calculated it on some post about 2 years ago, 100-200 grams IIRC). There may or may not be an efficiency loss, but no one seems to say there is an efficiency gain. Its quiet, but I wasn't aware a sync chain made noise.

Another thing about it is that it gets noticed right off. So, it starts a lot of (repetitive) conversations.