I couldn't find a definitive reference about that. In the comics they seem to have about the same height.
Batman is 6'2" and Superman is 6'3" according to dc.wikia.com.
I remember reading in a question to the comics (when some of theses were actually answered) ... I think it was around 1959 or 1960. The question was about Superman but the answer came back as Supes was 6' 2" tall and weighed 235#. The Bats was 6' 4" and 245#. Most readers here weren't even a thought in their parents dreams then but I am absolutely certain of that response because I thought it was so interesting and I had a near photographic memory in my youth.
I remember back in the 90's, when they were discussing one of the Tim Burton sequels, I went to a baseball game and Jose Canseco was playing. He was listed as 6'4" and 220 pounds. At the time, that was the exact listed height and weight for Bruce Wayne in the DC universe. I got rid of my collection from back then, so I can't find an official confirmation of those stats.