It is almost impossible to answer the question right now about Jay Cutler being a good fit for the Titans. There are a lot of other questions that have to be answered between now and then- mainly who the head coach is going to be.
For a minute, let's assume Mike Munchak is going to stay (a miserable thought, I know). If Munch stays, you have to assume that Dowell Loggains will stay as well. Loggains and Cutler apparently have a good relationship because it was reported that Cutler wanted the Bears to hire Loggains as the quarterback coach a couple of years ago. That interview never happened because Munchak blocked it.
Cutler can be a bit, how you say, enigmatic. If he is going to come here, it would be important for him to have a good relationship with the offensive coordinator. We can assume that would be the case with the current regime in place.
Again, all these questions have to be re-examined if there is a new staff *fingers crossed*.
Would Cutler be an upgrade over Jake Locker? I think Locker could develop into a player very similar to Cutler if Locker were able to stay healthy, but he hasn't been able to do that to this point. It just takes Locker too long to get back in the groove after an injury.
Cutler also has injury issues, but he can step right back in and play at a high level.
Is it better to sign Cutler than draft a guy? I say yes because Cutler still has some good years left, and the Titans have plenty of issues they need to address in the draft. If they can sign Cutler and draft a pass rusher in the first round (something they keep refusing to do even though it is an obvious, glaring need), they can compete in the AFC South next year.
Again, this could be much to do about nothing because Cutler might not ever hit the market, but the Titans should aggressively pursue him if he does.