fdlz: Most recurves are constructed with medium or high wrist grips, and most longbows with low wrist grips, and the type of grip determines how the bow should be held and shot.
But grip type really has nothing to do with where the center of the bow is. Whether the grip is in the center of the bow or not depends on how the bowyer crafts the bow, not the type of bow/grip it is. For example, most bowyers put the arrow rest about 1 1/4 - 1 3/8 inch above the center of the bow, regardless of whether they're building longbows or recurves. I know this because I've been measuring and recording bow centers for the past 10 years.
Also, keep in mind that this is center of the bow, not pivot point, which would likely be about 3/4 inch from the arrow shelf when the shelf is 1 1/4 above the center of the bow. But again, its position wouldn't vary from recurve to longbow, only the amount the riser is cut in or indexed at the pivot point. It will be much more indexed on medium and high wrist recurve risers.
Some bowyers may put the rest as much as 2 inches above the center of the bow. It's not terribly common on glass laminated bows, but they do exit, and it is quite common on self-bows because the bowyer often lets the bow's limbs determine which will be the top and bottom during the tillering process. With a 4-inch grip area, it's just a matter of flipping the bow end for end before cutting in the arrow shelf (2 inches above the center of the bow).
All bows, regardless of type, will bend the lower limb more if the grip isn't exactly in the center of the bow, i.e., the rest isn't 2 inches above the center of the bow, because the limbs are of unequal length with the lower limb being shorter. That's why bowyers generally incorporate a quarter inch or so of positive tiller into the top limb.