Run an A/B test, it's the only way to really know--regardless of what has worked for others or what has worked in the past--nothing beats testing.
If you don't want to test and just want an answer you might be in the wrong line of work but let me share my totally untested opinions anyway:
Panda punished sites with too many ads "above the fold," as long as these images are on the same domain they probably won't be considered ads.
<img /> images are considered content (unless quite small) and therefore should have alt text, they are also given higher priority in loading and rendering than CSS background images so there are accessibility and (contradictory) performance considerations. It's easier to scale HTML images but to control the cropping/positioning of background images.
Plain Ol' Semantic HTML
If these images are repeated frequently and mostly identical throughout the site then they are probably better suited to background images as they aren't really content, they are really navigation.
If these images are more targeted--offers that are highly relevant to the places where they are located--then they are part of the "content" of those pages and should be
<img /> images with alt text (for accessibility and usability).
I think @closetnoc is referring to title attributes (which are valid on any HTML element and generally display as tootltips on hover) but it's plausible he means the
<title> element of the page that the link points to.
I'm going to assume that he means title attribute and the jury is out on how much, if any, significance Google gives the title attribute (google it).
Google encourages using the title attribute on images, but nothing on using it on links (if you go the CSS background image method).
And there's plenty of claims that the title attribute is ineffective at influencing ranking and indexing, see here and here.
I don't know if I believe it has any SEO value at all (might have value to users) or not, which is why I encourage you to test and see.
Google is great at detecting and discounting patterns: think "duplicate content."
The more "unique" content you have the better so I suspect a mixture of the 2 techniques, with as much variation as possible in images, alt text and anchor text as possible will be the most effective.
A/B Testing to the Rescue!
Why guess when you can test?