People are saying Roger & Whitebeard for rivalries in one piece but almost no one mentioned Roger & Xebec. I would argue that those two possessed a greater (and more vicious) rivalry than Roger & WB. This is because the former are two members possessing the D. initial (likely branches of D clan) which would automatically equate to a clash of wills and interest in their goals. There is a possibility that Xebec constantly tried to recruit Roger to become either his right hand man or as a follower, much as Shiki would try many years later. When that didn't work out, Xebec could have been a huge thorn for Roger to deal with and eventually their paths crossed on God Valley.
Whitebeard never possessed the same dream that Roger had and never wished to pursue forbidden taboos or the truth about the world in the manner that Roger or Xebec did. He was offered all the information and location of Laugh tale on a silver platter but declined it besides asking for the meaning of the D. initial. If anything, WB and Roger became BFFs in a way, and Roger trusted/respected WB as much as he trusted Garp as if he was part of his crew.
