Well keep in mind the following
Title Tag = The title of your web page when it's search and found through engines. It also appears on the web browsers title bar/tab.
H1 = Does not necessary show up on search engines but within your web page. It is normally to create title at top of the page.
From my understanding and noting the differences above, search engines will value more the title tag than H1. However both are needed regardless.
Both serve a different purpose and both should be used correctly as they will help describe your site. Remember search engines look for quality and the user experience so I would recommend searching tips for writing a proper title, meta tags, etc..