Okay so here's my opinion on Bowser Jr.'s custom special moves.
-------NEUTRAL B-------
1. Shoots a slow moving, big cannonball.
2. Shoots a fast moving, tiny cannonball.
3. Shoots a gust of wind.
Okay so in my opinion 3 is just terrible. At first I thought it could be used to gimp or something, but the fact is, it takes like 90 years to startup and it's impossible to aim and use with that much startup. As for 1 and 2, 1 is obviously slower and stronger, 2 is obviously faster and weaker. While BJ could use a fast projectile, 2 has such a big startup that you wouldn't be able to use it how you would want to use a fast projectile, and since the startup basically makes it a slow projectile anyway, you might want the stronger one just because I think it makes it more effective. Either way it doesn't kill, though. To be honest neutral B just isn't gonna be his best move. I'm still experimenting, but I prefer 1 for now.
--------SIDE B--------
1. Fast startup, fast speed, good distance, long jump, driving damages a bit but spin-out doesn't
2. Fast startup, slow speed, small distance, tiny jump, driving damages, spin-out damages a lot and goes far
3. Slow startup, very fast speed, tiny tiny distance, driving buries opponents, spin-out does no damage but pushes them
This one is hard to pick. While 3 has the amazing bury, it's really telegraphed (slow startup) and easy to avoid (they literally just have to jump), so it's unlikely you'll hit with it in singles. Also the jump is tiny which is frustrating. With 2, the jump is also tiny, but the spin-out is really quite good. It goes far and can be semi-safe on shield. I still prefer 1 though, because of the jump. The spin-out does not damage, which sucks, but it's faster than 2 and jump is so good. It allows for a lot of mixups, especially when combined with DownB 1 (more on combinations later). That being said though, 2's spin-out does cover more options (like rolling) and keeps them in shield when they try to shield DownB 1, but the slow speed is what prevents it from being ideal. Ultimately I prefer 1.
--------UP B--------
1. Little startup, shoots up out of Car, Car explodes after a moment (if done in air it will fall a bit), goes high, good knockback
2. Bigger startup, shoots up out of Car, Car flies downward and explodes (meteors in air), doesn't go as high as 1, not as much knockback as 1
3. Little startup, flies upward, Car explodes and shoots Koopaling downward, goes high, great knockback
Out of all of these, you can do the hammer move in air, which is really good. Now, I don't like 3 that much. It's hard to hit with when they're in the air, and Bowser Jr. suffers without the free movement after the recovery. You can still hammer, but it's so fast that it's hard to aim. You're really unlikely to hit someone with this. As for 1 and 2, both are good. 1 goes higher, so yay. While 2 has more startup, the fact that it falls down is really good for edgeguarding. While you can stagespike with 1's explosion, it's easier to do it with 2 (plus it meteors). 1 is easier to hit with onstage due to the shorter startup (and it has good knockback). However, 2 combos into hammer REALLY WELL, making it easy to get kills. Due to this, I'd say in general 2 is better, but you might want the higher distance.
--------DOWN B--------
1. The Mechakoopa walks along the ground, turning at edges and eventually exploding. When it runs into an enemy it hits them up and explodes. Can be picked up and thrown.
2. Koopaling quickly throws the Mechakoopa, and it explodes on impact. It goes far, and if it doesn't hit anyone it stays in place and explodes quickly.
3. Big Mechakoopa that walks around. It eventually explodes, but won't hit an opponent it runs into. Can be picked up and thrown and it explodes on impact, and has lots of knockback.
Okay so this one is probably the one that's hardest to pick (other than maybe side special). They all act extremely differently. 1 is really good. You can deploy it and follow it with side-B and when it knocks them up and you can catch it with an aerial (that you hit them with) before it explodes and then throw it at them. You can also follow it and when they try to shield you can grab them. You can also pick it up and throw it; the best way to do that is by deploying it towards the edge and it'll turn around so you can pick it up immediately. Also you can drop it off the edge for an edgeguard. In general it's just a really good mix-up and is definitely the most versatile of the three. 2, meanwhile, is super fast. It starts fast and it flies fast. It's not very versatile though, but it's a really good projectile since it's so fast and has alright knockback. Definitely doesn't have the options and the mix-ups that 1 has. 3 is a really good kill option. It takes awhile to deploy but it's easy to pick up since it moves so slow. You throw it like an item and it kills pretty early. It's a good edgeguard option, but in neutral you don't always have time to deploy and pick it up. It also doesn't have the mixup options that 1 has. The biggest problem that all of them is that they aren't the other ones (lol). They're all really good, but choosing one means forgoing the other. 1 is crazy versatile and has a lot of mix-ups, 2 is super fast (and Bowser Jr. needs a fast projectile), and 3 is a solid kill option (which Bowser Jr. could use). I am still not sure what's best. I guess I just need to analyze BJ's weaknesses better and see what he needs. 2 and 3 are really good at what they do, but 1 is just so good and has so many options, so I think I'll stick with 1.
You ALSO don't want to be redundant. If you're using DownB 2, for example, you have a fast projectile and there's kind of no point to have Neutral B 2. The big jump for SideB 1 is really handy for quickly comboing from DownB 1. There's still a lot of deciding to do, especially in regards to DownB and SideB, but for now my set-up is going to be NeutralB 1, SideB 1, UpB 2, and DownB 1. I still might prefer NeutralB 2, SideB 2, UpB 1 is still solid, and any of the DownBs (I still need a lot more experimentation with them though to figure out which one handles BJ's problems better).
TL;DR Bowser Jr.'s custom specials are really good, the different DownBs are soooo different and good, we have to figure out what Bowser Jr. needs before picking custom specials.