Well, Mihawk is now scaled to a 12 Teraton feat.
Anyways, while Marth does have his regen, it's only when wielding Falchion, correct? Mihawk has spent his live contending against characters of equal or superior skill level, and he has not a single scar to show for it, and he is still carried in such high esteem. His display against other opponents shows his ability to exploit any openings presented, and he never overextends himself.
There's not a lot to go on for Mihawk's abilities, but if we just look at these two as fighters overall, Marth is going to slip up or be tricked by Mihawk, who would then cleave him in two with pinpoint accuracy. If Marth is disarmed of his blade after Mihawk realizes its healing factor, he'll go for the blade first before Marth.
Mihawk has Kenbunshoku haki, which will cover all of his blind spots, and he has Busoshoku haki to bolster his physical capabilities, as well as the power behind his blade.
Also, looking at Marth's profile, correct me if I'm wrong, but does he have Country level dura with the shield, and not his physical body? If that's the case, Mihawk merely needs to slip past Marth's guard once and cut him down, and if Marth manages to get through Mihawk's guard, Mihawk can take a hit w/ his durability, and possibly minimize the damage to nothing more than superficial with the use of haki on top of it.
How potent is Falchion's healing?
Until given more info on Marth's abilities, it seems as though Mihawk takes this.