By definition "payload" is "the amount of useful load (e.g. cargo, passengers, etc.) the plane can carry". Don't forget - the plane should also "carry" itself .

The total weight the plane can [safely] carry is "dirty weight" of the airplane (including fuel) plus payload. The rest is simple - more powerful engines should allow to carry more payload. Of course there are other factors, e.g. engine efficiency, etc., but I guess this is a jist of it.

In addition, other things being equal - the airplane with less "dirty weight" should be able to carry more "payload.