As someone who has a fast 802.11ac and has used NTRViewer with good success, I have to say that it comes nowhere close to being as good as a capture card for recording or viewing on a bigger screen. You can have decent (30+) FPS on one screen but the other screen will be a slideshow. Or you can have lower FPS on both screens, but a more consistent FPS between them. It might not matter that much to some people as most games don't use both screens actively, but NTR-CFW is certainly no replacement for a real capture card.
Personally, it really bothers me that the bottom screen is a slideshow even if I'm playing a game that primarily uses the top screen. It just looks bad.
It's possible that NTR-CFW could be improved further to get better FPS, but it will probably never be as good as a capture card.
@Dionicio3 A n3DS with NTR-CFW may be sufficient for your needs, and would be much, much cheaper than a capture card. Just be aware of the issue I mentioned. If you're really serious about streaming/recording or you want it to play on a bigger screen, and it's something you'll be using frequently, a capture card may be worth it.
Anyway, with capture card prices being as high as they are, I would say just to get a n3DS and mod that. There's no sense in modding outdated hardware when the mod costs several times more than the 3DS itself is worth and you can get the latest model and mod that instead for just a little more.
It has nothing to do with internet speed, but everything to do with the quality of your router and how congested your wifi network is (and in general how congested wifi is where you live)
