Having worked with both they have some of the same characteristics, only hickory is a harder, more dense wood. It's important when working either of these woods to pay close attention to the grain direction. Their fibers tend to tear rather than cut. I find it best to always work with the grain and skew the plane in these woods.
Ash does not have a distinctive heartwood, whereas hickory has a darker center as well as streaks of contrast. The colors are similar. Ash tends to be more blond while hickory is a bit more towards the grey tones. Spalted hickory can be an interesting choice if you want that look. Not sure how ash would be spalted. Ash would probably be more interesting quarter sawn than hickory.
I like both woods, but I've used ash most for furniture projects. My workbench top is 3" thick hickory (laminated). The top alone weighs about 250 lbs and is rock solid to work on. It shows little wear after 5 years of use.
Let us know what you decide and how the project goes. Always interested in hearing about others experiences.