Diagonal is slower than "normal" movement , but there is one thing where you can go faster with diagonal instead of straight movements.
There is a interesting thing about diagonal movement. when you move on diagonal there is a delay that usually slow your character , but if you go down on a stair or piramid or something where you change the floor that delay is more lower than the normal and you can move faster. You can try it on Thais for example , go down to the -1 stairs doing the diagonal movement and you will see that you can almost inmediatly go again diagonal.