They haven't been set up as enemies. Just because they're the only two Yonkou to be heavily involved since the timeskip doesn't pit them as enemies. Shanks not showing his full power means f*ck all. We haven't seen most characters full power, including Kaidou and Big Mom.1. Kaido and Big Mom are set up as enemies in the new arc/saga, that alone likely say that they are probably weaker than Shanks, who still will not show his full power. WB on the other hand was know as "Strongest Man in the World", he was defeated earlier in the series, but he was old geezer so that's nothing weird.
You really think Luffy will defeat Kaidou on his own? I call bullshit. Either Blackbeard (and his entire crew, in an 11 vs 1)will kill Kaidou and take his fruit (so Blackbeard has the strongest of each categoric class of fruit) or Luffy+Law (+Drake, potentially) will fight him in a 2(or 3) vs 1, by this point in the Manga, Law and Luffy will be way stronger than they are now, potentially being on Doffy's level individually.2. Shanks is Luffy's "mentor", or whatever to call it. Defeating Kaido would be next step being closer to Shanks + being "mentor" of main character is very important thing.
Shanks won't be killed off till later for multiple reasons in terms of story progression, returning the hat etc. nothing to do with strength. As you said earlier, the strongest Yonkou died first. So clearly power has nothing to do with the order in which they are defeated or killed off.
You just contradicted yourself. He clearly didn't fight Kaidou. There is no way two Yonkou can clash without injuries in that short a time. If they did fight then Kaidou wouldn't be worthy of his position as Yonkou. He's called the worlds strongest beast for a reason (a title which encompasses ALL living things).3. When Shanks arrived at MF, he was without a scratch, these two likely didn't fought, but just the case that Kaido didn't destroy Shanks and come to MF, to me say who is superior.
That clash is not worth mentioning since it lasted about 1 second. 1 clash of blades. Hardly a fight. Men are creatures, hence the title encompasses all living things. He was inferior to a former Whitebeard, it's not clear when Kaidou earnt this title. But Kaidou looked pretty confident about killing Whitebeard. He was stopped by Shanks; probably through a business deal. Kaidou clearly operates and relies on the underworld to support his wealth.4. WB was known as "Strongest Man in the World", Shanks clashed pretty good with him. Kaido is known as "Strongest Creature in the World", since he has "Creature" and not "Man", it mean that he is inferior to WB, and Shanks clashed pretty good with him.