I tried Mario Party Island Tour, Mario Kart 7
None of these games will work sadly, they both use DLplay-esque multiplayer, even if the game is installed on both consoles.
Mario Party Star Rush should work. but you're SOL trying to play MK7 that way. Install the same game, even if it's out of region for the other console, and when you try to multiplayer on the out of region one, it will say wireless connections are disabled.
I've tried this myself.
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I'm not sure, I tried playing Super C With my 3DS Of course mine is NEW 3DS USA = Super C JAP With download play. 3DS USA, didn't work. Everytime i go to download play with my game, it says to turn on wifi switch but is always on... So i doubt is possible, if anyone know how to make it work, i also be interested in knowing, unless i just have to rom inject the JAP game into USA cia, but i dunno how to do it either.
I don't think anyone's tried to fake a region like that, but yes. this is exactly what happens when DL-playing an out of region game. Either use games that have wireless/online multiplayer and avoid the DL-play ones, or do a Region Change for one of the consoles so that their regions MATCH.
EDIT: So to OP, re-read your post again and you say you have two consoles, one WITH CFW and one WITHOUT CFW, right?
You could Region Change the EUR console to be USA, so both would have the same region and that way you could DL-play with them, if you're willing to go thorough the hassle.
What CFW do you have? Luma?
How do you get into your CFW? Through DS settings, browser, menuhax, EmuNAND or a9lh?
Is your cfw on SYSNAND or EmuNAND?