I think that doing pulls with the palms facing away from you would increase your pulls with palms facing you, but not the other way around. You see, when you do them pronated(palms away), you are taking away a signifigant assist from the biceps, thus making the lats work harder. When you switch to the supinated grip(palms facing you), you are then adding a muscle group to aid the back in pulling the weight, which would obviously aid you in getting more reps, weight, whatever. However, if you concentrated on supinated grip pulls primarily, you would have a harder time doing pronated pulls, being that you are then subtracting that additional muscle group, thus causing you to have to rely on less muscle groups to aid in the pull.
If you want to increase your pull, and don't have the machine-aided pull(as these guys have already stated), then I would surely go with the supinated-grip(palms facing), in order to apply the most assistance to the back in order to complete the repetition(that assist being the biceps). If you can only get 1 or 2, then get them, then have a partner help you(I like to have people push on my middle back, rather than grab my ankles. Ankle-grabbing while spotting on pulls causes one to swing) force a couple more, then do a negative or 2. I'd start with those, and do 2 or 3 sets. They are tough if you're not natually adept to performing them. You'll get them though eventually there Private Pyle! J/K