Both groups have a love affair with ancient Judaism for some strange reason. The Mormons believe the Aaronic Priesthood was conferred upon Joseph and Hyrum Smith by the angel Moroni. The JW's regularly attempt to interpret the Law, sometimes in ways that would make a Pharisee cringe. (A good example is their stance on autologous transfusion)
Both groups have a fascination with ancient texts, but paradoxically, are not terribly knowledgeable about them. A Greek expression used by one and only one Bible writer is sprinkled throughout the Book of Mormon, which should set off alarm bells, but doesn't (The only way it could have gotten there is via the AV) There's nothing unusual about meeting an Evangelical Christian who can at least muddle his way through 1 John. It's very, very unusual to meet a JW who can.
Both groups believe they are chosen by God in a special way that sets them apart from other people. Both groups believe they are better people (morally and intellectually) than those in other religions, which (not surprisingly) results in a stunning level of arrogance.