The problem with trying to work out the gift and curse is that we are making the assumptions of what Dalinar would choose from the character we are shown in WoK. However I think that he went to Nightwatcher before the assassination of the King, and we know from numerous references that Dalinar was a completely different person before the assassination, before he started honouring the codes and before he started hearing passages from the way of kings. This makes it almost impossible to try and work out what sort of gift the old Dalinar would ask for.
However, from my reading of the book, I have a fairly strong suspicion that losing the memories of his wife wasn't the curse (or at least was not at the time, he may look back on it now and regret his decision). This leads me to the theory of whether the gift and curse can be the same thing. A loss of painful memories may be a gift at the time, but it could very soon become a curse.