From an accessible standpoint rather than an SEO standpoint, this is how it should work: An anchor's title is to describe where the anchor goes, displayable as a tooltip when hovering over it.
An image's title is to describe what the image is about, displayable as a tooltip when hovering over it.
An image's alt is to describe the image in such a way that it can be conveyed without seeing the picture itself, displayable in Lynx (text-only browser) or a screen-reader.
Because of that, I would include all three (albeit they may have slightly differing descriptions.)
As for the SEO, I'm not altogether sure, but I believe Google checks an anchor's title, as well as an image's title and alt attribute values :)
