Modernizr is a wonderful piece of software. I'm not familiar with HTML5 Boilerplate.
Fact of life — IE6 and IE7 are not going away anytime soon (IE6 still has greater usage worldwide than IE7.) Modernizer does reliable testing for specific feature support and makes the information available in an easy, systematic way to your CSS styles and JavaScript code. This is way better than using conditional IE comments and CSS hacks for dealing with IE6,7's incomplete and, for some properties, broken CSS.
Modernizer includes the Google HTML5 shim. This means that right now you can start using the new HTML5 semantic elements: section, article, aside, header, footer, nav and hgroup, without worrying about fallbacks for legacy browsers.
And, while it's nice to be able to test for specific CSS3 properties like border-radius, drop-shadow and transitions, I take care in my code that the page will still look good and work well without these presentation details.
On a side note, it's very encouraging to see the major browser makers focusing on improving their JavaScript performance and reliability. Google set the bar higher with Chrome. Firefox 4 beta feels 4 or 5 times faster than FF 3.6.
Larry