Why is Big Mom afraid of Shanks? Is it because of his ultimate Haki? Or is it because of the fact that he even survived after clashing with Edward Newgate and getting in a war with Kaido?
Big Mom is arguably the weakest Yonko, but she makes up with this by forming allies with different nation. Hence, the numbers of her offsprings.
Shanks is definitely a force to be feared with for good reasons.
- He has only 1 ship - He has only 1 ship** - As we currently know, Shanks only has a caveat of a crew in 1 single ship and that says a lot. Numbers in the OP world can mean a lot and him being in the New World with just a single ship and exceptional crews who are known to be great at Haki (Beckman, Lucky Roo and Yasopp).
- Former Cabin Boy of the Pirate King, Roger - He was known to be a part of Roger's Crew with Buggy, although this doesn't mean much because of the latter's credibility, being part of the crew might help him develop his Haki.
- Haki Strength - Shanks is shown to be a master of 2 types of Haki, Armament and especially Conqueror's Haki, greatly depicted when he boarded Whitebeard's ship. He also used to occassionaly fight with Mihawk, the World's Greatest Swordsman before his arm got decapitated.
Just this three alone, would make you fear the red-haired Pirate. Also, he intercepted Kaido's attempt to attack Whitebeard during the
Battle of Marineford and stopped said battle by just announcing the war is over which prompted Sengoku to do it which proves that Shanks is definitely someone you don't messed with.
If he can stop Kaido, the World Government/Marines, and make Blackbeard shiver then this just proves my point.
TL;DR Big Mom is afraid of Shanks because he's just too powerful for her.
I don't think Big Mom is afraid of Shanks. She was just being very cautious about him, and any other Yonko. She had a plan to take him down and any other Yonko by getting Lola married a giant Elbaf prince but failed to do so because Lola ran away from her.
She want the giant army, Germa 66 technologies, and all her alliance not because she's afraid with Shanks or any other yonko. But because she want a certain victory against them. She's not Luffy who would run against stronger opponent without thinking ahead...
Rather than the weakest Yonko, I would say that Big Mom is arguably the strongest. Indeed, she has never been defeated. Whitebeard was taken down by characters who wouldn't make Big Mom blink. Even if Kaido and Whitebeard are physically stronger, which I actually doubt, she has invulnerability far eclipsing Whitebeard and certainly Shanks. That doesn't even touch her Devil Fruit power and the god-like life-force she was born with. Or her Haki, which enabled her to demolish Gear Four Luffy in ONE BLOW.
Big mom could be the weakest Yonko because her power really revolves around fear. It has been shown that if you fear Big Mom, she can take your soul or life. But if you don’t fear her you can probably win against her. Since you aren’t effected by her power at all. There is still a chance that she can win by using haki and her size to her advantage.
So if other Yonko don’t fear her they could most definitely win if their skilled enough and can put match her in haki. And be able to cut her think skin.
The mystery surrounding Shanks' powers and capabilities is suffocating in a sense. Compared to Big M, I think Shanks would win. First of all, the Yonkou rarely attack each other which makes a head to head comparison quite difficult. It is, however, important to note that Shanks' straw hat is basically the star of the show. Power recognizes power. The hat belonged to someone else before Shanks, guess who? This cannot be used as concrete evidence but it definitely means something. Also, Shanks could hold his own against Mihawk, White Beard and Kaido's forces despite not having a devil fruit ability. Even Black Beard needs time to gather enough strength to challenge him and that speaks volumes. In conclusion, the other Yonkou might be extremely powerful but everyone in the OP world, from the government to the navy and the Yonkou themselves, recognizes that Shanks is in a league of his own. Remember, this is just a biased opinion so do not treat it like concrete fact from statements in OP.