I have a 3DS XL, got it in late January and am using a 16GB SDHC card. I also went through the eShop to update the system. Had no errors and everything went fine.
Miiverse itself is web-based on the Wii U. They could make it a native app, but it is more likely to be web-based.
EDIT: Since I'm on the top of this page, gonna post this again:
Maybe post more info about your 3DS's? Are they an XL? When did you purchase it? Where did you access the update from (eShop or system settings)? Are you using a stock SD card? And some other stuff that could be related.
Not following you. :/ Wouldn't Miiverse be a standalone native app, and be more like the eShop in that regard?
Miiverse itself is web-based on the Wii U. They could make it a native app, but it is more likely to be web-based.
EDIT: Since I'm on the top of this page, gonna post this again:
Maybe post more info about your 3DS's? Are they an XL? When did you purchase it? Where did you access the update from (eShop or system settings)? Are you using a stock SD card? And some other stuff that could be related.