If those two world ever met, what do you think will happen?
I'll tell you what would happen: Akatsuki and Issei will meet each other, and fight each other. What will the outcome be, you asked? Here's an answer for you: Akatsuki beats Issei...to a pulp. You're welcome.
Okay, then who do you think will get along with whom in both series?
For HYNE, Akatsuki and Miu. As for HS DxD...ah, who cares, Issei will never end up with any girl.
I meant, as which series character will get along with the other series character. Like would Issei and Akatsuki get along or Miu and Rias etc?
Miu and Rias getting along? Maybe, I dunno. But Akatsuki and Issei? Hardly.
Take "Fairy Tail X Rave Master", for example. Natsu and Haru fought each other, and ended up not getting along. So...yeah, Akatsuki and Issei will be enemies.
What about Toriko and Luffy, they became great friends?
HYNE and HS DxD (if that crossover ever exist) will end up like Fairy Tail X Rave Master, not like One Piece X Toriko.