My views here do not apply to every single agnostic and atheist, but rather it applies to each group, on average.
When it comes to mundane or ordinary claims, both atheists and agnostics tend to deal with them reasonably. But as we move towards the more controversial or extraordinary claims, then this is where I've seen a difference between the two groups.
I tend to find that agnostics are more open-minded than atheists. When it comes to anecdotal or even extraordinary claims (e.g. ghost sighting claims), agnostics do not become dismissive. They are usually willing to explore the credible points (or areas that arent disproven) and build on those areas.
In contrast, I find that many atheists tend to be highly skeptical to dismissive when it comes to anecdotal or claims involving something extraordinary. The worse case examples are those that are only interested in debunking or dismissing these types of claims, as opposed to trying to build on the plausible parts.
One thing that I like to get into is why people believe or think certain ways. I believe that many atheists accept materialism as being the correct view of reality. So the only things that are possible would be those things that are consistent or compatible with that view. In contrast, agnostics usually don't have a fixed metaphysical view of reality (they don't limit themselves to materialism, at least), and as such, things that seem to defy materialism are not considered impossible. This is why you'll tend to find more agnostics being willing to entertain and explore religion, the spiritual, or even supernatural matters.
One thing I recently came to the conclusion about was in how atheists will resort to the 'bottom line' in their defense of position, when atheism is criticized.
For example - someone might observe "atheists are always 'such and such'" and the reply "No. Atheism is simply the lack of beliefs in god/gods"
The contrast between the behavior of those calling themselves atheists and the position itself leads to confusion for those trying to understand the position, because many times atheists make remarks which suggest they have reason to defend their position - normally as the best position - and make statements which clearly overstep the simply position of lacking belief in gods.
Because of this confusion-causing tactic from many atheists I have encountered, I no longer refer to them as 'atheists' but as 'materialists' because it is obvious that is what they practice, and since atheism isn't a practice but a position, it removes any confusion from the mix.