<title> VS <h1>

which is most important in terms of keyword weight for SEO out of the title tag and the h1 tag?

Titles bear a more significant weight than the header tags. I would say both are very important in terms of SEO.

How they relate:
Title->book title
Headers->book chapters and sub chapters

Hope it helps

Title is more important than h1. kepp in mind don't ignore H1 tag.

when it come to search engine it matters

but surely the title of the page should be the same as the h1? only difference benig that title tag is part of invisible head, h1 part of visible body?

i also think that title seems to carry more weight though...

Not exactly.. Title is what search engines look at upon visiting a site to first determine its nature content. Headers are there to reinforce the related content. Please see below for an example:

Where does anchor text figure in the "importance" table?
And ALT text?

Anchor text is more of an off-page optimization and its weightage differs from on the search engines. Google places great emphasis on inbound links so I would say that anchor text is far more important than any on-page optimization in Google. To illustrate an example, query 'failure' in Google and we will see the effect of off-page optimizing for the first result..

Alt attributes are more for the images so that Google can 'read' the image for easier content relevancy allocation. I don't think alt is more important than the titles and headers.