Mihawk holds the title of "World's Greatest Swordsman" and, as such, it is beyond any doubt that his swordsmanship skills are superior to those of Shanks. This was, once again, brought up in One Piece 1058 where he was specifically compared to Shanks.
In the same chapter, One Piece shows its readers first the incredible power of Shanks and then his only weakness: his grand fleet.
Currently, however, Shanks is likely stronger than Luffy, simply due to the fact that the plot demands that of him. Luffy has not surpassed Shanks just yet, otherwise, their future fight would hold no significant value.
Shanks is probably way above Zoro`s level. Of all the characters still alive in One Piece, Dracule Mihawk is undoubtedly the strongest swordsman in the world. After all, he holds the title. Vista was the commander of the fifth division of Whitebeard`s Pirates and was considered the best swordsman in Whitebeard`s crew.
As one of the Four Emperors, he cannot let just any pirate roam freely after directly clashing with him. Not to mention, Shanks wins the fight fair and square. If Kid was stronger, he wouldn't hesitate to destroy the Red Hair Pirates.
Currently it should be Shanks. Shanks is narratively depicted to be as strong as old Whitebeard. Garp is at best at that level, both being previous Roger's rivals. But that should also mean that prime Garp was stronger than prime (current) Shanks, since Shanks, as hyped as fans want him to be, isn't Roger level.
As seen in his battle with Sakazuki, Shanks can use armament haki to imbue his sword with this power. Shanks can proficiently use observation haki as well, thus, making him one of the strongest haki users in the One Piece anime series.
Shanks possesses the ability to use Kenbunshoku Haki, as revealed in his vivre card and has almost unrivalled mastery over it. He is known for being the Killer of Observation Haki as he is able to stop people from being able to use it as seen from Kidd.
Despite not having a Devil Fruit power, Shanks is an extremely powerful pirate with skill that far surpasses most in the One Piece world. In combat, Shanks doesn't seem to rely on much. He carries a sword with him and, although not confirmed, it appears to be one of the Saijo o Wazamono grade swords.
It is a known fact that Kaido has lost to his fellow Yonko and the Navy a combined 7 times and been captured a total of 18 times. While Kaido might be the strongest in terms of raw strength, there are definitely those who can beat him a fight. Write for Us!
Shanks' scar caused by Blackbeard because he's mistaking the gomu no mi with yami no mi which Blackbeard been searching for decades.
With its powers, Luffy was able to topple even Kaido and if he could defeat the man who was the Strongest Creature Alive, he can certainly defeat Shanks as well.
1 Luffy Vs.
The fight is, undoubtedly, the most difficult one that Luffy has fought so far. Kaido managed to defeat Luffy three times. For the first time, Luffy faced defeat against him Kuri and was thrown in prison. There, he learned Internal Destruction Ryuo and took Kaido on during the Onigashima Raid.
One Piece Data Books - Shanks did not lose any power losing an arm.
It is evident that the only person capable of surpassing Roger is Luffy. Even though Luffy still has a lot to achieve, he is the only person who can transform the entire world.
I don't think you can simply say "he can beat an admiral" because even within the Admirals, there's such a huge difference in power. I personally think that Luffy could probably just barely beat Aokoji now (or in the near future), and he could fight but not beat Kizaru, and has no chance of beating Akainu.
Gear 10th Luffy is Luffy's ultimate form from the upcoming speculative fan-made sequel to One Piece, Son of the Pirate King. Luffy has continuously trained his haki and Devil Fruit powers during his time as Pirate King until he achieved this gear.
Shanks has clashed against Kaido when the latter tried to reach Marineford. It is very likely that Shanks would be able to injure Kaido in this battle.
It's still unknown if he ever won/lost to shanks, however, they're known as rivals. It's safe to say that they were equal in combat, until shanks lost an arm.