Several reasons why I think that
1. Shanks ran with Roger and Rayleigh, both likely the two greatest swordsmen in their time, possibly Rayleigh is still top ten even at his old age? Maybe. But the point is, from a very young age Shanks saw how it was done versus every powerful crew in Roger's path
2. He ended a war with his presence alone. Nobody dared to go against him. There wasn't one single character at Marineford who even thought about it in what was shown
3. He goes head to head with Kaido and shows up to Marineford not much long after. This guy is beyond strong
4. Mihawk was curious as to how strong Whitebeard was and gave him a small test, in which Diamond Jozu deflected aeay from his Captain. Mihawk doesn't know what going up against a Yonko in a true fight is like. I think Mihawk and Shanks are training partners more or less, and their fights were more like practice than anything. Shanks has fought Kaido and held his own with no apparent damage. A standstill
There is no reason for me to think that Mihawk would defeat Shanks in a sword fight that I have heard yet
Vista held his own versus Mihawk and I think Shanks is mich more powerful. It's fun to think about how powerful Shanks is, but we have to rely on such little information. Still, something tells me he's a monster even with one arm
I cannot wait until the next arc or two...We will likely see Big Mom and Shanks in full action versus Luffy during the next two future arcs is my guess since this is the Yonko saga