It depends on what you want. BigBlueMenu is a modified devmenu, NASA is mainly for those without EmuNAND, and FBI is picky about what CIAs you can install with it but also allows you to install directly over a network. I use both BBM and FBI.
NASA can now install over wifi, and in batches. Open NASA on your 3DS, point Houston to a folder with all your CIAs in it, go to work or have a nap ... Everything installed without having to touch your SD card or worry about deleting the CIAs afterwards!
BBM has the perk of properly installing certain things, like custom theme cias, whereas FBI allows to do more dangerous stuff (which is helpful if you know what you're doing), such as uninstalling NAND titles.
Edit: I should say, I've not used NASA, so I can't voice my opinion on that
devmenu. the only time i use fbi was when i region changing my emunand.
i hope one day we'll have a true powerful and user friendly homebrew cia manager.
- nand access like fbi, but on a whole separate menu with big red warning (it's really easy to accidentally push trigger button and change installation target from sd to nand)
- can overwrite installed programs like old devmenu (i personally use old dev menu to install new patched version mhx), or even better, if possible, when a title is already exist, there's option on what to do.
- recognized unique/title id and display it as game/program title in "human language" like nasa, or even better, if we have option to record and name the file we're currently installing so when we want to delete it, it'll be easy to find.
To be fair I've no idea if it was updated using ChoidujourNX, but that look like it. I also can't seem to use Daybreak on a SX Core so lol. Also pardon if talking about the switch here makes you uncomfortable