Well we also know Blackbeard likes to taunt people, it's his one biggest weakness that we've seen in the series so far and has always lead to him receiving a lot of damage he didn't need to.
Itachi's a genius and would use the sword of totsuka straight away if he found out that it was the only way to win the battle. As for not using it quickly, he used it fairly fast against Nagato and the only reason he would've held it back for so long against Sasuke was because he was waiting for Orochimaru to come out. In fact my counter arguement to people saying he doesn't use it early would be that as soon as Orochimaru came out, Itachi sealed him before he could even finish his sentence.
I'd say given that they're both in character, Itachi has a good chance of winning this even though Blackbeard could wipe him out in one attack.
You can survive the genjutsu if you are strong willed. Blackbeard carries the will of D and is tough enough to take a quake from whitebeard to the face. What can itachi really do to him?
Surviving genjutsu has nothing to do with willpower, Kakashi is extrememly strong willed and Tsukuyomi k.o'ed him in seconds.
@taichokage: I agree that Tsykuyomi won't take down Blackbeard like it would Kakashi, the pain thresholds in One Piece in general seem to be greater than Naruto's, I was simply stating that Blackbeard most likely isn't going to break out of it with willpower alone, he might however tolerate it until Itachi becomes exhausted.
@GoldenStar66: I would think then that Itachi has little to maybe moderate difficulty winning here. Any Genjutsu especially Tsuyokomi could end BB. Regular genjutsu might be countered by strong will but it takes a sharingan to counter Tsuyokomi. Susano with the sword of Totsuka and Yates mirror would also prove doom for BB. Amatarasu would at least be useful in setting up a winning move, and Itachi could always use one of those crazy desperation dojutsu (inzagi or inzami or whatever). The fact that he's edo means physical attacks (like quakes) would be next to useless.
Anyone mentioning Edo, there's no mention of it in the OP for battle conditions and the photo above clearly shows Itachi alive and well. So don't even factor it in for this match.
Otherwise, I'm inclined to agree that Blackbeard would be a bit much for Itachi to handle in terms of stats and the abilities of his Devil Fruits. Only hope for Itachi is striking down Blackbeard with Susanoo's Totsuka Sword, which he won't do right away unless he is aware of how powerful his foe is and Blackbeard's overconfidence leading him to take a blow from the sword.