I use both. I find that getting large websites indexed in Bing will require submitting an XML Sitemap to Bing webmaster tools regardless of how good your site architecture it.   Alternatively - I always use Google Webmaster Tools.  Primarily for the messages sent directly from Google, duplicate titles/descriptions and lab tools.

I'm ashamed to admit that I don't use Bing Webmaster Tools at all. On second thought, no I'm not.

My philosophy is to optimize for Google first and foremost. Bing organic referrals are a like icing on the cake but not a significant focus in the grand scheme of marketing.

Hugo - Thats exactly how I look at it too.  It's not until I noticed the issue with indexing did I start messing with Bing.  As mentioned earlier though its just with extremely large sites.  Bings search spiders just aren't as sophisticated as Googles.

Google Webmaster Tools is the source I use most often.  Since GWT integrated domain/site access with profiles already granted access to Google Analytics, it has become the the easiest to activate.  Bing Webmaster Tools can be a pain to activate and sometimes, depending on the site data contained in BWT, not worth it over just using GWT alone.

Now all that being said, I do like Bing's tool set and would use it way more if it was easier to activate.

I like some the of functionality in Bing Webmaster Tools, but in my opinion their user interface is horrible, one of if not the worst webmaster tool interfaces out there. If they would clean it up and make it easier to use and segment and filter data I would use it more.

I am constantly amazed at how much work they continue to put into adding new functionality and data points yet continue to ignore the UI.

The UI definitely falls short of anything that could be considered enterprise level worthy.