I agree with ExNavyPilot, I really don't think you can go wrong with either park. It probably comes down to deciding which one feels like it draws you to it the most.
I think the two parks have a similar feel about them, or at least it seems that way to me. Shiloh is probably a little more isolated, but maybe not by a lot. There's more war-related history to see around Chattanooga than Shiloh, although the area around Shiloh has some other interesting history of its own to check out. And you'd want to get down to Corinth as well, if you visit Shiloh.
As others have said, Lookout Mountain is a can't-miss visit if you go with Chickamauga. I pretty much got hooked on the war at Point Park, so it has a special place for me. But really, either park is going to be a good choice.
You mentioned being interested in the Hornet's Nest at Shiloh. It's a pretty easy walk along the Sunken Road through the woods there, around half-a-mile one-way. The ground is fairly level for the most part. And you can also, if you wish, walk along the Eastern Corinth Road through that area, re-tracing the Confederate advance toward the Sunken Road Line. A lot more to see of the park outside this area of course, but I understand the special draw it can have for people.
Enjoy your visit, whichever park you choose. I don't think you can go wrong either way.
Perry