"Taking seriously" is a wrong expression
"look for a fight" is more appropriate
and my answer to this is a No, cause I don't think Oda intends to show you who is superior to who when it comes to those two
Oda loves inconclusiveness when it comes to top tiers.. where you never get your satisfactory answer
Hell, even in his way of giving titles... you can see that with the "Strongest man" or "strongest creature"... in other words, he's giving a way out for himself to play more with things than giving you a definitive answer
In other words, Oda is following Thorkell logic from Vinland Saga if you've seen it... when the prince asked him if he was weaker than both of Askeladd and Thorfinn since he lost to Thorfinn while Thorfinn lost to Askeladd... Thorkell explained that it's not something as easily explained as that
Point is... to Mihawk's perspective... if he fought Shanks, if he defeated him, he will not have a true taste of victory due to the missing arm... which is why Mihawk is not interested. It's never about whether Shanks now is weaker than him or he got stronger over the years or whatever... it's just a fight Mihawk doesn't see a good outcome from it regardless
So, unless Shanks got back that arm, Mihawk will never regain his interest imo. regardless of how muc power up Shanks gets... Mihawk can also still get stronger and power up too in his own view... so, it's just the arm thingy