It's not about their rivalry, Shanks is clearly a swordsman and Mihawk is the strongest in that domain even when Shanks is around. It doesn't matter if they hadn't fought for years, when one of them is clearly acknowledged to be the strongest. Mihawk is being seen as the strongest SM by the entire world, despite the fact that there is a yonko who's also a swordsman.
It doesn't make any sense for Mihawk to be the weaker one even if you try to evaluate their strength using their rivalry as a reference; They should be equals or at least comparable in strength 10 years ago. Then it's Shanks who lost the most of the two, when there is nothing that can interrupt Mihawk's growth. Shanks lost his dominant arm, which'd make a substantial difference, He was forced to adjust himself to fight using his right arm. He had to adopt an entirly different fighting method. However, Mihawk remained the same and grown stronger with no problems at all. Not to mention, that loosing an arm will have an effect on how efficently one can fight, especially, when you're a swordsman. It's practically impossible for him to be still stronger than Miahwk unless his growth rate is leaps above that of Mihawk which again is very unlikely as Mihawk is also one of the 3 yongest top tier fighters.