Both councils, insofar as they spoke on matters of dogma and doctrine as the infallible Magisterium are completely correct in every way.  Dogma has never changed, and never will.  The infallible and inerrant church does not make mistakes on dogma.  Any confusion is because the differences, if there are any, were not actually statements of dogma or doctrine, they just appeared to be so to the uninitiated lay person, or they aren't actually in conflict, but just appear to be and it can all be explained with lengthy logically sound arguments.  Many learned church scholars have been employed dealing with such matters, in keeping with Jesus' teachings that his church was to expend any resources necessary on theological points and academic work and finding employment for clergy scholars who don't want to mess around with people and their mundane problems.  I think he also mentioned taking care of the poor, etc., but his focus was on academia.