Strictly better means more or less the same as always better.
That's not what people normally mean when they say strictly better, though; the number of card pairs where one is truly strictly better than the other becomes infinitesimal if that's your definition. What people normally mean is that card X is strictly better than card Y if card X is better commonly enough that it would be bad game design for both cards to cost the same.
This is not what strictly better means and not how the majority of people apply the term (as there is already a term,
on average better or just
better without an absolutey predicate like strictly in front of it). In game theory it means the same as
choice/strategy A dominates choice/strategy B independent of what the opponent does. So using this for Dominion means that a card A is strictly better than a card B when there is no Kingdom in which this is not the case.
Hunting Party is on average better than Laboratory but not strictly better. Just like Highway is on average better than Peddler but not strictly better.
By the way, I am totally against constructing weird fringe cases that occur with a very small probability to prove that something is not strictly better; that's just pointless nonsense.
One example the Diadem-Storyteller thing in the other thread and another would be the claim that e.g. Farming Village is not strictly better than Village due to Shepherd or Oppulent Castle. I'd categorize this under insignificant.
Another example to illustrate (this really no so hard to understand difference between absolutes and averages) is comparing cards of roughly equivalent strength. For example it makes absolutely no sense to claim that Mountain Village is strictly better than Farming Village but I guess most people would agree that it is on average the better card.