Time affects flames, and I don't see any particular way that Yamamoto could win this. He's certainly stronger, but that's not enough by itself.

I have a feeling that Yamamoto-sama would win.

Honestly, I don't get why Yamamoto is winning with that really big difference in this poll.
It's like you all were so sure that he would win.

But I'm not so sure. Baraggan proved to be one of the hardest enemies to defeat, not just because of his experience (as he's surely potentially old like Yamamoto) but also because he surpasses Yamamoto's abilities. Exactly as whiteflame55 said.

I don't see the big deal of the Pyro Gramp when he get to confront an enemy like Baraggan who can rot and make grow old everything in his path.

I guess to beat Baraggan you need more than a title that says 'I'm the Head-Captain'. I guess it takes wayyyyy much more. It takes technique, different and really special abilities, a sharp intelect (and probably 2, as shown in the Soi Fong and Hachi battle).
Or either, you'll need a different type of Zanpakuto (maybe Illusion type like Aizen-sama's) but not a fire zanpakuto.