Blackbeard wins this.
You saw how easily Shanks blocked Akainu's punch... now, remember BB left that scar on Shanks and Shanks even said that he wasn't being careless in their fight either..
Shanks became a Yonko before BB, but only because BB was patiently waiting to start his master plan. BB is a beast.. and obviously deserves his Yonko position.. and he earned it by a landslide, considering after WB died, there was barely any other pirate around that was worthy enough to take WB's Yonko seat..
Akainu however, just baaaarrreeellllyyyy earned his most recent title.. considering Kuzan was very close to earning it as well..
Based on portrayal, BlackBeard is slightly above Akainu in both strength and skill.
Not really. When Blackbeard blocked WB's powers and WB only had his bisento available, Teach got his chest carved in and rendered helpless from one blow from the Bisento. Meanwhile, Akainu blocked a Bisento WITH a Quake infused into it with one leg. If we really wanna go by portrayal, then Akainu is stronger than Teach.
There's also the fact that Fleet Admiral and Yonko aren't purely attained by power. Being Fleet Admiral has as much to do with leadership as it does with strength, and is nothing more than an Admiral who has upstanding leadership skills that fit the Navy's needs. Kuzan and Akainu settled their conflict with battle because it's not like they were gonna have a debate convention. You definitely need to be strong, but it's not like being World's Strongest Swordsman or World's Strongest Man.
Same kind of applies for Yonko. Teach became a Yonko after his crew defeated the WB pirates. Not something that falls on BB individually. Don't get me wrong, you DEFINITELY need strength to be a Yonko, but the method of achieving it in BB's case isn't so much a testament to his individual strength as it is to his entire crew's strength as a whole.
When it comes to in battle, Akainu is a terrible match-up for Blackbeard in all honesty. When it comes to the Yami Yami no Mi, Teach needs to drag him in close and grab him. For a man that oozes magma, that's really risky. When Teach tried to pull in Ace, he got two flaming spears lodged into his chest that Ace threw as he was being pulled. Now replace Ace with Akainu and replace the spears with Akainu throwing meteors towards Teach as he's pulled through the air. Someone as careless as Teach isn't gonna do well pulling someone like Akainu in close through the air, especially since Akainu's attacks can remove entire limbs.
When it comes to the Gura Gura no Mi, Akainu took two of the strongest Quakes WB produced during the entire war, a man who's had it for decades, and Akainu emerged with the strength to fight all of WB's commanders except for two and didn't receive any new or significant damage. I doubt Teach is gonna produce so much power that Quakes alone with **** Akainu up.