Neither of those are legitimate debates. Tannehill and Tyrod Taylor have both proven repeatedly that they are abject failures as starting NFL quarterbacks. Teddy has proven, twice now, the exact opposite.
Perhaps the Titans think "the light has come on" for Tannehill and thus sign him because he's cheap, knows their system, and "finally figured it out". They would be absolute stupid idiots if so, but maybe they think that.
There is not a single person who makes their living in the NFL that would ever say "hmm.. would I rather have Tyrod Taylor or Teddy Bridgewater?!", except maybe whoever runs the drafts for the Browns. Same thing for Tannehill and anyone that doesn't live in Nashville.