Actually, for Japanese sets unlimited editions are overall harder to come by, rarer and more expensive. There are exceptions of course, but for most Japanese sets that have both a 1st and unlimited edition print run, UED is harder to find.
Here is also a relevant thread for Japanese sets without a 1st edition run; without an unlimited edition run; or for which we know for sure UED is rarer than 1st: www.elitefourum.com/t/1st-edition-timeline-lets-iron-it-out/16054/1 (which I also mention in my 1st edition stamps article).
Although I’m not too familiar with the Japanese Aquapolis set you’ve mentioned, I’m pretty sure UED is rarer for that set in comparison to 1st edition as well. It’s definitely the case for Skyridge (the set after it), and Expedition Base Set (the set before) is kinda a special case where the UED were only handed out as promos or special event cards (see this article) and are probably the rarest UED Japanese cards that are out there (although L2/L3/Champions Pack cards are also pretty damn hard to find in UED).
Greetz,
Quuador