Yes, mainly the orientation of the biner thing and another advantage is the abrasion from the bridge gets spread around all the inside of the ring because it moves.
On a biner you always abrade the same spot.
I know its not a big issue (except on Aramid-cover rope- bridges)...
I run the small Rock Exotica rigging plate on my bridge btw.
Nice for clipping in different components.
Some guys like to have a small swivel on their bridge. Good for multiple components as well and no twist in it (as with the plate sometimes). I may change to that in the future as well, although I am really pleased with the TriRig so far.