there's not anything like a "legit" and "ilegal" cia installers, you are confusing both of those terms with "Legit Cias", which are Cias Which can be installed in your 3DS withouth having to use a CFW, although not every cia can be a Legit Cia, they are limited.
here you can find everything related to it:
https://gbatemp.net/threads/what-is-a-legit-cia-and-other-noob-cia-questions-answered.386705/
It seems like you need to read that yourself my man. Jesus Christ.
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Anyways..the only thing that makes FBI or anything that was not written by Nintendo
"legal" is because it was coded someone that was outside of Nintendo without using Nintendo's code. Hence, making it legal.
BUT, if anything that was copyrighted within the program: EX: Code, images, etc. It will be considered "illegal". The issue with illegal CIA installers (The only illegal one beings Nintendo's self-written code) is that they are not updated unlike legal ones. (Once again, coded by people in recent times, instead of SDK tools from 2011 or whatever. Old stuff.) So, they will get updated more often, with more bug fixes. The thing about Nintendo's installer though is that it much more quick and more accurate with installing things people say. Also, have better rates with installing patches and downloadable content with illegal ones, (once again, Nintendo's). FBI, etc, have more features. (EX: Installing over WIFI, installing batches of files.)
So,
tl;dr
Legal = More features, potentially more bugs since the code is being touched by random people sometimes. (I think? Github..does that? I don't know. I don't use github).
illegal = Less features, works better
some most of the time, faster
some of the time.
