Akainu is winning this. Akainu even without his fruit has advanced armament Haki and BB so far hasn't shown any form of advanced Haki. On top of all of this, Akainu is quite durable and has pretty great endurance and can fight against another admiral for 10 whole days. Blackbeard hasn't shown that kind of stamina yet and on top of all of this, Akainu knows about his DF and his abilities so he'd be wary and likely play the smart game. But so would Blackbeard. The problem with Blackbeard is that he gets way to over confident and that could lead to his downfall. Augur stated this himself when they were fighting against Law and his crew. Law himself managed to even get in a few attacks on Blackbeard, so I'm most certainly sure Akainu can do the exact same but on a whole more deadly scale.