Gateway "should" work on the New 3DS in the future.
Gateway supports homebrew

, and eshop dumps. Sky3DS does not. BUT if you use Gateway on the New 3DS you will have to keep your firmware on 9.2 or below indefinitely. You WILL get to use the latest firmware, but every time you want to run the latest firmware, or even use your Gateway cart for that matter, you will have to go online and load a corrupt page in the 3DS web browser, or load something from a local server set up by your android phone or whatever ppl have been developing idk I haven't been paying attention. It's not as bad as it sounds, cause you can just leave your 3DS on all the time in sleep mode.
Sky3DS will work on the latest firmware without anything special just like any official 3DS card will. Honestly, it'll probably work on every firmware ever. You switch games by pressing a button on the Sky3DS cart, which takes a while to cycle through games. BUT, the Sky3DS cart will NOT play homebrew or eshop dumps. It is a piracy/backup browser ONLY.
Then there's MT-Cart, which is kind of cute. It's like Gateway but worse, but they are a lot nicer than Gateway and release their hacks to people without their cart and don't try to brick people so if you like that you can support them. I'm only 80% sure they support the latest firmware though.