simple break down.
N3ds for n3ds only games and better play for some games like zelda mm. (because of the c-stick)
The bad is you have to get a first wave one in order to get a low firmware like 9.0 or 9.2
Gateway is more for homebrew and it supports alot of games off the bad (cia eshop, drag and drop adding)
Sky3ds is mainly for playing retail games. The great thing about it is it works on all firmwares.