Okay, so I couldn't figure out how to do it, so I ended up with 3 different entries in the EmulationStation.
I'm leaving instructions and the *.svg files I made just in case anyone wants to recreate my scenario.
3 Entries on EmulationStation:
FBA Capcom Fighting Games, mapped for SNES-style controllers (4 face buttons + 2 shoulder buttons; 8bitdo SNES sn30, 8bitdo NES n30)
FBA Capcom Fighting Games, mapped for Saturn-style controllers (6 face buttons + 2 shoulder buttons; RetroBit Saturn Pad, RetroBit Genesis Arcade Pad, 8bitdo Mega Drive m30, Sega Saturn USB Pad, Retroflag Classic Controller)
FBA Capcom Fighting Games, mapped for PlayStation-style controllers (4 face buttons + 4 shoulder buttons; DualShock, DualShock 2, DualShock 3, DualShock 4, Xbox 360 controller, Xbox One controller, Hori Fighting Commander, Hori Real Arcade Pro, Brook Universal Stick or pretty much any arcade stick that follows the standard layout)
That way you can use whatever controller you have available and the button layout will always be correct for those fighting games.
1st Step - Add the Systems on es_systems.cfg
<system>
<name>capcomf4</name>
<fullname>Final Burn Alpha</fullname>
<path>/home/pi/RetroPie/roms/capcom-fighting</path>
<extension>.7z .cue .fba .iso .zip .7Z .CUE .FBA .ISO .ZIP</extension>
<command>/opt/retropie/supplementary/runcommand/runcommand.sh 0 _SYS_ capcomf4 %ROM%</command>
<platform>arcade</platform>
<theme>capcomf4</theme>
</system>
<system>
<name>capcomf6</name>
<fullname>Final Burn Alpha</fullname>
<path>/home/pi/RetroPie/roms/capcom-fighting</path>
<extension>.7z .cue .fba .iso .zip .7Z .CUE .FBA .ISO .ZIP</extension>
<command>/opt/retropie/supplementary/runcommand/runcommand.sh 0 _SYS_ capcomf6 %ROM%</command>
<platform>arcade</platform>
<theme>capcomf6</theme>
</system>
<system>
<name>capcomfpsx</name>
<fullname>Final Burn Alpha</fullname>
<path>/home/pi/RetroPie/roms/capcom-fighting</path>
<extension>.7z .cue .fba .iso .zip .7Z .CUE .FBA .ISO .ZIP</extension>
<command>/opt/retropie/supplementary/runcommand/runcommand.sh 0 _SYS_ capcomfpsx %ROM%</command>
<platform>arcade</platform>
<theme>capcomfpsx</theme>
</system>
2nd Step - Add the Themes Files
https://www62.zippyshare.com/v/wMXwTxNE/file.html
Just copy to the folder /etc/emulationstation/themes/carbon
3rd Step - Add the Emulation Settings
https://www69.zippyshare.com/v/2HnpWDWb/file.html
Just copy to the folder /opt/retropie/configs
The remap info are in those files. Just a reminder, your controllers have to set according to the wiki https://github.com/RetroPie/RetroPie-Setup/wiki, for instance, the Left Shoulder is mapped to the first button to the left on the top row of your controller.
4th Step - Create Folder and Copy ROMs
You'll need a folder called capcom-fighting and drop your ROMs there.
If you're using Arcade Manager, here's the *.cvs file of the non-merged ROMs I used:
name;
dstlku;
hsf2;
hsf2j;
jojo;
jojoba;
jojobane;
jojoj;
mbomberj;
mbombrdj;
megaman;
megaman2;
mshj;
mshu;
mshvsfj;
mshvsfu;
mvscjsing;
mvscu;
nwarru;
redearth;
rockman2j;
rockmanj;
sf;
sf2cejc;
sf2ceuc;
sf2hf;
sf2hfj;
sf2jl;
sf2uk;
sfa2u;
sfa3u;
sfau;
sfiii2;
sfiii2j;
sfiii3n;
sfiii3u;
sfiiij;
sfiiiu;
sfj;
sfz2alj;
sfz2j;
sfz3j;
sfzj;
smbomb;
ssf2t;
ssf2tb;
ssf2tbj;
ssf2xj;
vampj;
vhunt2;
vhuntj;
vsav2;
vsavj;
vsavu;
warzard;
xmcotaj;
xmcotau;
xmvsfj;
xmvsfu;
Also, EmulationStation doesn't seem to respect any order other than alphabetically, so I numbered the games in my gamelist.xml
Well, that should be it. Unfortunatelly it won't let me play fighting games against someone who owns a different controller than the one I decide to use, but at the very least I have everything mapped and ready for use.
Also I am aware that Street Fighter The Movie runs well and uses a 6-button layout but... I guess I rather not remember that exists.