In detail, what allowed the Europeans to achieve dominance in the New World but remain marginal, except as naval powers, in the east?
This is a interesting question...
First, you would have to define a time period. I would hardly call Europe's influence of the far east to be marginal during the 1800's...though they didn't supplant the local population their colonial efforts helped shape places like India, China, Vietnam, and the middle east.
I am guessing that the question is relating more toward the colonial period in America's history, a time when the "new world" was the focus of Europe's exploitive efforts.
I would imagine that one of the reason that the Europeans were successful at dominating North and South America was the fact that much of the local populations were killed through either the upheaval that ruined their societal base or disease. Large numbers of natives simply died due to germs, leaving chunks of New England sparsely populated. All the Europeans had to do was to insert their own settlers and presto change-o...the land took on a European flavor.
Technology played a part as well...the natives of North and South America had advanced cultures but not as much as the Europeans (never having had the opportunity to acquire their technology through trade.) Europe had trading ties to the East and therefore shared technological advances with them (and vice-versa.)
Distance would have been a factor...land travel was very slow and the route to get to the East overland was dangerous, long, and crossed many hostile areas. Travel to the new world was done by ship which was, comparatively, faster and safer. But to get to the East from Europe one either had to sail around Africa or around South America...both daunting prospects. For this reason it would have been more expedient and cost effective to concentrate colonial efforts on the Americas. The question itself kind of supports this..."except as naval powers." The only way they wanted to get there was by ship, and no country is able to suppress another by naval power alone.
Lastly, you could make an argument that after the colonization of North and South America the Europeans were not so keen on trying to transplant the populations necessary to "dominate" another culture. I mean, look what happened to the American colonies...they broke away! And the Spanish lost most of South America. It became simpler for the Europeans to run their colonies with the minimum number of people needed to exploit a regions resources rather than try to achieve absolute "dominance" over other parts of the world.