An undisputable method is to do a comparative benchmark (provided you do it correctly and the other party is not bad faith). Don't care about theoretical complexities.
Otherwise you will spend a hard time convincing someone who doesn't see the obvious: a shift moves every element once, while two reversals move it twice.
By the way, a shift is optimal, as every element has to move at least once. And if properly implemented as a memmov, it is very fast (while a single reversal cannot be as fast).