Post pics of your house IMO 15' opening is almost like no wall at all so I would not do casing.

Will you always have the same wall color or other wall treatment in both spaces? If you think you’d ever paint them different colors or shades of one color, use trim. Otherwise you’ll be visiting the Decorating forum here to ask where to make the change.

Just don't do it like the reclaimed beam kitchen--it looks like they put the kitchen in an old closet and then removed the doors. :)

But seriously, I have cased and uncased openings in my home and find that the cased ones are easier to keep clean. If there is a chance of anyone cutting the turns too close, go with cased.

I currently blame my children. In the past I have had indoor-outdoor cats who left rub marks on openings.

I did all my openings cased as I also think they are easier to keep clean (specially when painted in semi-gloss paint) and less prone to damage. Wood casing is stronger than drywall, if clipped on the corner by a hard object. My largest cased opening is 14 ft and the smallest 38".

After looking at your photos again, my question is why all that ceiling height and then you just did normal height windows?

A lot depends upon the design of the house. What did the designer of the house have in mind?