I have been using the Japanese Badge center in 9.5.0 for a long while. I think you'll be just fine with the older version considering that that one is also more likely to get further hacking access eventually.
The reason the older older versions already have residual information for the badge center is due to it being release in Japan way earlier and they just happened to have left it in the US update, so you should have all the features. The bigger concern for you is that the e-shop is not working right now for older versions without kernel access, but hopefully someone will find a work around soon.
I suggest either way you stay on 10.1 to try and keep as many extra features that you can have.