[/QUOTE]Shanks isn't better than Mihawk at anything, don't get it confused, none of these fanmade notions exist in the story. Doesn't mean that shanks isn't on par with Mihawk but he's not on the winning side.[/QUOTE]
Just wait to feel dumb. Shanks has no desire for a swordsman title, his kingly ambition is related to joyboy and ushering forth the new Era. Mihawk only uses his haki to improve his swordsmanship and maintain his title of the world greatest swordsman, shanks uses all types of haki to ensure overall combat superiority so that he was able to maintain the balance and keep the gears spinning towards luffy fulfilling some joyboy profacy. It's pretty obvious really, mihawk is a better swordsman with haki strong enough to withstand shanks and best him with his superior swordsmanship he just uses his haki 1 dimensionally, whereas shanks used his haki in every way possible to achieve a different goal, hence why mihawk lost interest in fighting shanks who is a worthy rival but has no desire to further his swordsmanship because of other ambitions.