Personally, I don't there should be a hard limit on how many branches are published for each game, or even a soft limit along the lines of "when you reach this number of movies, it's time to start seriously question new branches" Instead, I like to focus on significant gameplay differences, or "compelling differences" like the Judge Guidelines say.
In my personal experience, route differences are usually less noticeable unless they are drastically different, and I mean
drastically. What stands out more and I feel is a better criteria is looking at the techniques used.
Does a new branch consistently apply techniques that are not present in the current branches? Let's use the Ring Attack runs as an example, since I saw those contested earlier. One of the byproducts of collecting every ring is that a large portion of the level needs to be visited, so just naturally with that goal, some techniques, like for example glitching to the end of the level become less useful. I'm feeling the effect of that on the Aero the Acrobat 2 100% run I'm currently working on. In the any% run, wall zips were the way to beat most levels. However, in 100%, when I have to visit most of the map anyway, they become much less useful. It doesn't mean that the move is disallowed, just that the goal changes the usefulness of the technique.
We've had a few runs rejected because they didn't apply techniques that weren't present in the published movies, even if it makes a different route or is highly optimized. A really good example of this is
#5978: The_Tas_Master's N64 The Legend of Zelda: Ocarina of Time "All Medallions" in 53:21.70. While it's reliance on techniques that weren't present in other branches wasn't the only reason that movie was rejected, it's still a significant one. One that's more in line with this submission is
#1572: mr_roberts_z's N64 Super Mario 64 "Coinless-Cannonless-Capless" in 1:03:10.80, which people also felt was too similar to published movies.
Like a few others, I watched the currently published "Sonic and Tails" TAS and compared it with this TAS and the Tails only TAS level by level, noting where things changed. Keep in mind, that the casual viewer is not going to look at these things in that amount of detail. They are going to watch the entire movie and mostly go by feel, and if it feels the same as a published movie, it might as well be the same.
Since Sonic and Tails has access to Tail's moveset, I was expecting Tail's techniques to be similar to the any% movie. I was pleasantly surprised to find that Tail's levels actually do feel quite different for the most part. Enough that I believe a new branch is justified for the category. Sonic alone, however, didn't.
I think it was about 2/3s of the way through the Sonic 3 portion where I thought of a big reason for this. Everything that Sonic can do Sonic and Tails can do as well. It's just that Sonic alone doesn't have access to Tail's moveset. With this in mind, the run is less of a run with a different character and more like Sonic and Tails, but Sonic is not allowed to use Tails.
Movies where the moveset of a character is limited in some way can, should, and have been accepted for publication if the limit leads to different solutions in almost every circumstance. Movies like
[1868] SNES Super Mario World "no powerups, maximum exits" by PangaeaPanga in 1:18:23.22,
[2062] N64 Super Mario 64 "70 stars, no Backwards Long Jump" by Jesus, Kyman, MICKEY_Vis11189, MoltovM, Nahoc, snark, sonicpacker, ToT, CeeSammerZ, coin2884, Eru, Goronem, Mokkori, Nekuran, Nothing693 & pasta in 42:58.52, or to use a non Mario example,
[3375] SNES Disney's Aladdin "capeless" by jaysmad in 16:36.78 are accepted because limiting the moveset like this removes a tool that was used constantly in the other runs to the detriment of all other possibilities. So oddly removing options actually leads to increased variety of techniques employed in almost the entire run. I noticed in the any% movie that Sonic relies on Tails a lot less than I initially thought, and unless he's using Tails, the solutions are going to be the same as a Sonic only run.
In terms of different characters being justified for branches, let me use another game to help provide a barometer for my limits. In
Super Mario Bros 2 (US version), I don't think there's any reason to have a Toad only, Luigi only, or Mario only run. Peach only is much more justified. Even though all four characters play differently, Peach is the only one with a noticeable unique ability. She can float, which leads to significant changes. I see no reason why the others would be really unique in that regard, even though Luigi's extra jump height does give him different route options in some levels.
Also, very minor point that shouldn't have bearing, but I feel is worth mentioning:
the speedrun.com leaderboard for this game lumps Sonic solo and Sonic and Tails into the same category.
One small thing I find disappointing is the currently published any% is five and a half years old, and watching the submission in comparison to that, I can really see the difference that those years make in understanding the game and adding further optimization. The improvements this movie makes really should be represented in a published Sonic 3 and Knuckles TAS. I don't think this movie is different enough to justify a new branch, but if we could find any way to publish this movie without adding new branches, I think we should make that happen. I also would be interested to see a level by level breakdown for how this compares to the currently published any%, especially to see if it's actually faster on any levels.