You can approach this question this way:
Let's assign arbitrary values of strength to both Mihawk and Shanks, also assume that Shanks has both arms to begin with.
Mihawk = 50
Shanks = 50
They are both equal. I think this is the implication that Databook/VC/Magazine is trying to give when it says:
"世界一の剣豪と肩を並べたほどの実力を持つ。"
"He was once as powerful as the best swordsman in the world."
But then, Shanks loses his arm.
So now,
Mihawk = 50
Shanks = 45 (-5 due to arm loss)
Shanks is now weaker than Mihawk because losing his arm made him weaker.
"片腕になろうと勢力衰えず!"
"I can be a one-armed man and still be a force to be reckoned with! "
The implication here is that he did in fact get weaker, however, he is still strong.
Notice how I only did (-5) and not (-3,000,000,000,000). Shanks didn't turn into fodder.
However, give both of them x amount of years to progress (+40 for both). (Note: This is also assuming that you think they have gotten stronger since the time when they dueled).
Mihawk = 90
Shanks = 85
Now they have both gotten stronger, but it remains that Mihawk is still ahead of Shanks. Hence why he's the World's strongest swordsman. As a result of Mihawk's title, they are still in a sense rivals, because Shanks is a swordsman too.
Notice here how Roger and Buggy are "ex-captain" and "ex-comrade". Mihawk isn't "ex-rival", he is simply just "rival".
While Shanks is still weaker than Mihawk, he himself is strong. So with the help of a crew (just like Kaido, BM, BB and WB), he is able to become an emperor.
There's a pretty good reason why people think Mihawk can fight top tiers without actually having any panels of him fighting top tiers. It's the same reason why people think Ryokugyu can fight top tiers without having any panels of him fighting top tiers.
Mihawk has a title that puts him above certain top tiers so the most reasonable assumption to make is that he can indeed fight these top tiers despite never having done so.
I think most normal readers didn't think much of these interactions. Especially since equal clashes don't imply much and aren't really indicative of how an extended fight would go on.
Overall, I just want Oda to give us more details on this Shanks-Mihawk stuff. Just need definitive answers.