A thicker bar for presses (overhead, benches, etc) sets a bit differently in the palm, as Chaos suggested. More towards the heel of the hand, where better leverage is obtained and less stress on the wrist.
Some guy's will do presses (push presses) allowing the bar (regular or thicker) to rest on the heel of the hand, giving a more direct inlinement with the wrist and forearms. And in return more power. Using a thumbles grip of course. Lot of heavier bencher's will include this method in training. Gripping a bar (thumbs around the bar) too tightly also can limit full strength in some exercises.
If the bar on the heel of the hands is new to you, may want to proceed with caution at first. After awhile the bar sets very well with this thumbles method and the wrist more flexable. Might try using powder or stick-up with this (plese wipe the bar after use...some guy's don't). If possible, inside a PR at first or spotters if doing BP's.
Martial artist know the value and power of hitting with the heel of the hands in close quarter fighting, getting much more power to the strike. Football linemen also. Good Luck.
