Which side is up? Is there a right and wrong? Is one side a better
"grade"
but pieced together and the other side a worse grade but in wider sheets?

I've hunted the net and found many pages discussing how veneer is cut,
but nothing explaining which side is up.

Generally there is a "better side". The "big-sheet side" is rotory cut. It
is likely the lesser grade side. Rotory cut IMHO (and apparently yours too)
looks inferior because perpetually flatsawn wood does not exist in nature
and therefore looks "not quite right".

That said, there is nothing that says you can't use the rotory cut side if
that suited you. Choose the side based on which looks best to you.

-Steve