Which wood will burn better this winter?

If you have a very dry fall, the uncovered wood may burn OK but the wood in the shed should burn much better. I would wait for a good dry spell, then tarp the wood that is uncovered. At the very least, put some plywood or something that will keep the rain off it from now until you need it this winter.
In my experience, rain on stacked wood is OK in the summer but you want it dry in the fall. Do not wrap the wood in the tarp, just on top so the rain will not fall on it. Wet wood from rain is not the same as wet wood from unseasoned wood. Rain water will dry in a few weeks of good, dry air flow.

Nice stacks! That wood shed is beautiful. I think the open air wood will burn better. But honestly based on the reviews on the site, Ash seasons pretty quickly, and I think you're in good shape either way.

If your uncovered wood experienced a lot more airflow, it may be more seasoned (lower cellular moisture) than the shed wood. Just guessing.

As a test, you can re-split a few logs and check in the split with a moisture meter.

FWIW, years ago, I did a burn test in my outdoor firepit at various seasoning times for red oak. I simply observed how much hissing and smoke the wood gave off. It wasn't scientifically rigorous, but it gave me some practical information on red oak seasoning times.