Math competition for grades 1 through 6

A friend is seeking information about math competitions for grades 1-6.  Does anyone have specific knowledge or experience with these?  Are some better known than others are?  Any advice on which one is the best?  Are there significant differences in the types of questions asked?

Here are some that appear to be popular:

• Continental Math League , grades 2-9
• Math League, grades 4-12
• Math Olympiads for Elementary & Middle Schools (MOEMS), grades 4-8

Some previous KTM math competition discussions:
http://kitchentablemath.blogspot.com/2009/10/math-competitions.html
http://kitchentablemath.blogspot.com/2008/10/mathcounts.html