Union by Rank vs Union by Size


I was studying Union Find, and according to Wikipedia, there are 2 types of Union: Union by rank and Union by size. My question is, what is the runtime different between the 2(if any)?

Intuitively it feels like Union by size would always be better, since each time we merge, we are increasing the rank of every node in one tree by 1, and to minimize overall runtime, we want to increase that one tree to be the one with smaller number of nodes, even though the final tree height might be greater.

But does this make a big difference in runtime?