The Lone Eagle and the Competitor are similar in appearance, but I think that the Competitor is the more refined of the two. Advantages over the Lone Eagle include:

1) No cocking lever on the Competitor. It cocks when you open the breech.

2) The Competitor, at least the later production model that I have, has a much better trigger than the Lone Eagles that I have seen/handled.

3) This is fairly subjective, and varies depending upon the barrel, but the Competitor always seemed like it balanced better than the Lone Eagle.

I don't believe that there are any common parts between the two. They are completely different designs.