Either will show water rings or marks because it's still wood--it's the *finish (stain, paint, varnish, whatever) that will protect better (or worse) against rings etc.

Having had both solid and veneer tables, I would say that solid would be more durable than veneer. I had to be very careful around my veneer table and still ended up snapping off a piece of the top veneer by accidentally catching the edge with a cleaning cloth. And this was a seldom used dining table in a house without children!

I don't know about the brands that you mention but a hardwood table with a good finish will last. Our friends have an oak table with a marine spar finish, along with lots of grandkids and company, and that table looks great after 10 years. YMMV

Amish over Ashley, no contest.

Wood is wood and it is not uncommon for wood furniture to have veneers which use exotic woods for design purposes.

If you are using the table every day - especially with children - I would recommend having the table finished with what is called a bar top finish. It is extremely durable and more impervious to water issues than standard finishes. However, it is not a license to abuse the table as you should still use trivets for hot stuff and use placemats, coasters or other items to protect against moisture.

Without knowing more I would suspect that a hand crafted solid wood table made by Amish crafts people is better than Ashley although I know nothing specifically about that brand.

I am finishing a remodel and had my dining table custom made by a local wood worker to my specifications and design and I am thrilled with the results. It wasn't cheap but was far less expensive than a comparable quality and design would have cost if I could have even found one I like in the stores.