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From a technical standpoint, I assume the HREF TITLE attribute is supposed to be bound to the link destination, while the IMG ALT attribute is to describe the image itself, but since we are looking to provide accurate context, it's difficult sometimes.
Do search engine bots treat the attributes differently? What happens when both are identical? Should they be different?
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 :)