drop bear
Sr. Grandmaster
In our case, a different branch of Aikido is not directly related. Ueshiba's Aikido is separately derived from Daito-ryu. So expecting them to be equivalent wouldn't be realistic. Many of their schools only use black and white. Those that have other belts don't even use the same colors as NGA. There's no reason arts should look for equivalency when they don't share the same technique set, ranks, and focus. What would we be equivalent in?? NGA will show similar skill levels at a given rank, even between associations (and most independent schools), in my experience.
This is where your analogy fails. BJJ is still all the same style, with just variations. That would be more like comparing Takemusu Association's Aikido with USAF's Aikido (I think these work - not familiar with them). Two different associations, but similar approach to ranking, so you can expect similar results at a given rank. The same problem exists in Karate, perhaps. Different schools have a different focus, so use the ranks a bit differently. Even if there was a 20-man Kumite requirement for all of them, each would likely choose different rules for that Kumite, which would still lead to different levels of competency in different areas. The only way you could make them more equivalent would be to have competition be a central theme, and use the BJJ model of who you can hold you own with defines your rank. There's merit in that, but it requires competition to be effective between schools.
There is of course competition between schools. formal and informal. And your rank in BJJ is your rank everywhere. If you go from a gracie to a machado school. you dont get a white belt.