How competitive are US National Teams against other countries?The diplomatic answer, is "not very".
The undiplomatic answer, "not at all".
National team can be broken into three fairly distint tiers of quality. The first tier consists primarily of European teams, with a few others (notably Egypt-Men and South Korea-Women). The second and third tiers basically consists of the rest of the world, minus the noted exceptions. When first tier teams play second tier teams the game might be close for awhile, but in the end the first tier team's experience results in a comfortable victory of 5-10 goals. When a first tier team plays a third tier team it is generally a blow out in which the first tier team can pretty much decide what they want the final score to be. (As an analogy, think original USA Dream Team Basketball vs Angola)
Historically, the US has alternated between the second and third tier. Currently, the US is clearly in the third tier. Recent results in Pan American Championships certainly support this assessment. In July, the Men's Team finished 7th out of 8 teams at the Pan American Championships in Chile. The US had a 1-4 record and lost to the 2nd place team, Brazil 31-13 in Pool Play. Last year the Women's team placed 4th in the same competition. The Women's Junior team this past Summer finished 7th out of 7 teams and lost by an average of 28 goals. Keep in mind, too, that none of the Pan American Teams are in the first tier and only the Brazilian and Argentinian Men's and Women's Program can be considered 2nd tier. (Although, an argument can be made, based on recent World Championship performances, that they may be poised for a breakthrough to the first tier. It will be interesting to see how Brazil does at the Olympics.)
US National teams have not always performed so poorly. In the 1980's and 90's the US was a second team tier and usually placed 1st or 2nd at Pan Am championships. Performance in the Olympics and World Championships varied between a 2nd tier or 3rd tier performance. As a point of reference the World Championships team I played for in 1993 lost every game they played by 16 or more goals-- clearly a 3rd tier performance. In Atlanta, the Men's team played to some measure of respectability, placing 9th. The Women's team also has had periods of respectability. At the LA Olympics in 1984, the Women placed 4th, although they benefitted from a weaker field due to the Communist Boycot.
To sum up, the US can be characterized as a team, that while at times has shown promise, has consistently been at the back of the pack.