The advantages of going to conference committee include the fact that the finished product returning becomes non-amendable (though it can still be filibustered in the Senate). You can fast-track the conference report onto the floor without going through the committee process. And most important to me, you can provide some transparency in these negotiations that has been lacking. Conference committees are often pro forma processes, with the real work going on behind the scenes, but members of the conference committee still have to vote on any changes, in public view.
A conference committee will at least create a forum for the debate in public rather than in cloistered back rooms.