I think a lot of us tend to lean towards Twitter Bootstrap these days, but HTML5 BP has always done some pretty cool stuff around standardising the structure of your project.
I’d love to see more sites integrate both as an ideal starting point.
To me, HTML5 BP and Twitter Bootstrap are two entirely different monkeys. I like to use a hybrid of both, using the Initalizr service. HTML5 BP contains a very good Apache settings (.htaccess) with solid explanations, among other standards-based code/markup and the ant build script. On the other hand, Twitter Bootstrap is all about visual elements, responsiveness, and jQuery plugins. I think that you can have the best of both worlds by integrating the two to work in tandem.
The advantage of Twitter bootstrap is it gives you a set of styles by dropping in a single class to your markup. Any other style can do the same, would love to see it happen.