Basically the Japanese Victory cup is very similar to modern Japanese trophies like the XY Victory Ring, Victory Decoration and Victory Proof in that usually less than 100 (you can read the specific estimates in each Bulbapedia article) were given out for each place. For the cups it’s around 40 each.
The English one was more in line with the Medals you mentioned, likely even more distributed. They’ve been awarded in many more, much smaller tournaments, like Gym Challenge promos.
Visual difference: The Japanese cups have a Snowflake rainbow holo pattern, as well as holo borders and a regional holographic stamp that is gold, silver or bronze depending on placing. The English have the English play promo reverse holo style, a date stamp, and non-holographic borders (sad).
Award difference: The English distribution method was similar to the English Victory Medals you mentioned. Battle Roads at least here in USA were low-stakes, casual style local tournaments, lower stature than City Championship. In Japan the Battle Roads are high-stakes competititive regional tournaments.
Thanks for the info. With what y’all are saying I would have expected way more graded English copies than there currently are in the pop. Figured more people would be interested as it is a prize card and the art is pretty nice.
The idea of more “affordable prize cards” didn’t start to be more fleshed out until after PSA was completely inundated with cards from what I’ve seen. These cards were a few bucks each at best. Now there is definitely more demand but it’s going to take a while for them to get through grading.