Is there a performance gain from using exclusively transpose vs complex conjugate transpose?

Intuitively it would appear that performing fewer operations would make a function faster, but this may not be the case for this particular operation. I suspect that for vectors and matrices with fewer elements there is probably little difference in performance between the two operations. Should there be a difference in the two operations at which point, in terms of number of elements I'm transposing, should I consider using exclusive transpose, .', vs complex conjugate transpose, '?

Thanks