There absolutely is a correct way, and lots of incorrect ways to hold the hoods. Its all in the wrists.

Hoods too low means you have to move your wrists into ulnar deviation which can result in locked elbows/shrugged shoulders and cause neck and shoulder pain.

Your wrist should be neutral - not flexed or extended. Extended wrists (hands bent back) can be caused by bars which are too wide or a frame/stem too long.

The wrist in this picture is correct...



Bike fit can typically fix most issues but sometimes it is a matter of form. I flexed my wrists a lot when I got my first real road bike and had to just work on proper form. Eventually it became second nature.

Bike and Body: Have neck and shoulder pain on the bike?

Wrist Movements