Saying you should not focus on Bing/Yahoo is bad advice. But keep sharing it and let those of us who work with both benefit more
Also the crawler has nothing to do with why your site is indexed "faster" or "better" than another. Just like Google Bing/Yahoo would like certain things as well, while most things with Google transfer over there are things you should be doing to cater just to them. Look into using the OpenGraph Protocol and Schema protocols, just too start. Then learn what their algo's are searching for and why you are failing.
@Original Poster - With the information you have shared there is not enough to give you better advice.