The other week, I reported that with Google News specifically, the recommendation is that your titles and H1s be consistent.
Now a Google Webmaster Help thread has people asking if the title and the H1 (header) tags need to be exactly the same or identical.
The answer is that “consistent” doesn’t mean “identical.” With Google News, you probably want to keep them almost exactly the same. But with normal Google web search, having them close is fine.
Personally, I like to use a more explanatory but shorter headline with my stories here and a more keyword based title so that people who are looking for help with this topic can find it in Google. But often, the titles here and H1s here are consistent, maybe not exactly identical.