The difference obviously lies in the personalities and age difference.
Similar age:
Roger/Rayleigh
Shanks/Benn
Luffy/Zoro
Kidd/Killer
Big age difference:
Whitebeard/Marco
Big Mom/Kata
Kaido/King
Based on this the Vice Captains get treated differently. For those in a similar age they talk pretty much on the same level with each other, while with a big age difference they have a parent/child relationship, so pretty much a dominant one.
=> That's the simple reason. Best proof is Oden who was worlds below Newgate when he joined his crew, but Newgate called him "brother". It's just age and personality based and has 0% any influence in the strength.