I would go with Dragon on this. For me Whitebeard, Shanks, Akainu, Aokiji and Dragon are in a league apart from others. Mihawk is strong but from what we saw in the war Luffy was able to avoid his attacks and Mihawk didn't go easy on Luffy. I wouldn't say it would be the same (pre time skip) if its Akainu or one in the above leauge. Even though nothing more about Dragon was shown except stopping Smoker, I would say Dragon is stronger than Mihawk. He even gained powerful alies like Kuma, ivankov etc.,
Mihawk probably wins. He's supposed to be as strong as Shanks and that's pretty strong. Besides, we saw almost nothing of Dragon.
Fight goes like this
Mihawk spots Dragon
Mihawk on the floor all worn out, sword broken, and spewing bubbles from mouth
Dragon did not bother to take off his hood.
Dragon: ( Some strong pirates eh?) ...
I vote Dragon because well...He is Luffy's dad and I don't see anyone but the absolute strongest beating him.
Hype is such a powerful thing.
Dragon will most certainly take this one. Simple reasons being are Kuma, who can easily be considered as strong as Mihawk, was Dragon's subordinate. During the marineford fight, almost all of the famous pirates/marines were shocked to hear Luffy was Dragon's son, not due to Luffy's fame. however, Dragon's. Smoker, who is not afraid to challenge Shichibukai Hancock when she stopped him attacking the same person as Dragon did, did not dare to even face off Dragon. Mihawk is definitely one of the top tier characters, just not the toppest like Dragon.
Well, Dragon should be at least around Admirals level. Otherwise, he wouldn't have been a threat to the WG.
And I actually think that Mihawk would be weaker than Dragon. Still, it's not good to post a character we don't know much about as a fighter.
True we should not judge on characters we have not seen in real battle. But indication towards Dragon's ability isnt just based on his title as the "Most wanted man". There are many hints towards his powers.