This is how I see it:
The <title> is for the user to see the page title in search engines and the OS (task bar, title bar, bookmarks).
The <h1> is for user the see the page title in the content.
I format mine like this:
<title>Page Title: Website Name</title>
<h1>Page Title</h1>
That way:
- Keywords are reinforced.
- The user sees the title on page, in search engines, and in the OS.
- The user sees what website the page came from.
- Limited 'duplicate' page title penalty by search engines. That's why the website name is at the end.
[EDIT]
After reading a few comments I wanted to note that I'll often put my tags in the "wrong" order in code. To inform the search engine what's more important. I've heard this is "bad" but I can't verify that.
If I have a site layout like:
Animals > Dogs > Breeds > Labrador Retriever
<title>Labrador Retriever: The Animal Site</title>
...
<h6>Dog Breeds</h6>
...
<h1>Labrador Retriever</h1>
I've told the search engine that the page is about Labrador Retrievers but that there is a minor importance to Dog Breeds...but it's still important.