I don't know. We've seen Luffy and Zoro and Luffy and Ussop fighting seriously. Shit can happen between close friends. I mean, a "jolly pirate" will fight anybody who gets in the way of his goals.

We know that Roger and Whitebeard were at least friendly, if not friends (I am guessing they were... Roger offered to give Whitebeard directions to Raftel, but Whitebeard wasn't even interested in it.) One the other hand, we know they have fought duels against each other. Since they're both "jolly pirates", we can assume that their duels came about since their goals conflicted, but that it wasn't "personal", and that they stopped fighting as soon as their goals stopped conflicting.

I guess the point I'm making is that Shanks versus Mihawk could have been "serious", but that they needn't become enemies just because they have fought in the past. Even now, they're on opposite sides of a war, specifically because Shanks realized that Blackbeard was using the WG to tip the balance of the world. And you can be (pretty) sure that if Mihawk and Shanks end up facing off, they'll fight seriously, despite the fact that Mihawk surely realized it (about Blackbeard) too.