Well, maybe. Depends on which you're referring to, and for what mode.
Keep in mind, the following is all just my opinion, and could be completely incorrect. Also keep in mind, the following is pretty long, so there's a TLDR at the bottom of the post if you don't feel like reading all of it.
For Turf War, all are fine, though for different reasons. Vanilla Inkbrush has unparallelled speed while brushing and Sprinkler/Inkstrike to snag large areas quickly, though you want to avoid combat outside of ambushing and faces competition from the N-Zap '89 due to having the same loadout (the '89 lacks speed while attacking, but has better range, allowing it to function in combat). Inkbrush Nouveau isn't as good for inking turf, but its Ink Mines can hold areas or surprise nearby attackers and Bubbler is good for passing to teammates; it's a support weapon, but not terrible. The Octobrush trades speed for a bit more range and respectable power, though it still moves fairly quickly, can use Squid Beakons to get fallen teammates (or yourself) back into the fight faster, and it has Kraken for when you're cornered, though it still shouldn't be winning in direct combat against anything above Splattershot range without Kraken.
For Splat Zones, the Vanilla Inkbrush's turf-covering and ambushing capabilities can be very annoying, but in non-ambush combat it's useless, so it has to stick to inking, which it's good at, but it can't really help in combat without serious stealth skills; it's certainly usable, but difficult. The Inkbrush Nouveau has to play pure defense unless it has a Bubbler, dropping Ink Mines in a Zone and ambushing foes as they come for them, and passing Bubbler to teammates when it gets popped (or popping when it's attacked), and it has no way to harass at range due to its loadout (Vanilla at least has Sprinkler/Inkstrike to try to take Zones from a distance); it's usable, but I wouldn't pick it over the original. The Octobrush is serviceable in combat, though you should still stick to ambushes mostly due to your still-shortish range, but it excels at supporting your team with well-placed Beakons, inking up Zones quickly with its larger swings, and annoying enemies with the Kraken; definitely usable, though the Krak-On Splat Roller is good competition for it (trading speed for power and a bit more range), though both are alright in my opinion.
For Tower Control, the Vanilla Inkbrush is out of its element; it can throw Sprinklers on the tower to ink areas passively as it moves and drop Inkstrikes on an enemy-controlled Tower to free it up for your teammates to retake it, but your lack of range means you'll struggle to hit anything on the tower without Inkstriking it or climbing on, which can be risky; it has its strengths, but I wouldn't recommend it. The Inkbrush Nouveau is better on the Tower, with Ink Mines to keep its top covered in your ink and splat inkvaders trying to get on and Bubbler to keep yourself alive on the Tower (thus pushing it forward a bit more), but your lack of range means you're a sitting duck to Chargers and Blasters looking to shoot the Tower (though Bubbler can alleviate this briefly); it's a decent pick, at least in my opinion. The Octobrush has decent power and some range, letting it attempt to fight back against close-up attackers to the Tower, and its Squid Beakons can give teammates flanking opportunities along the Tower's route or get them on the Tower without leaving an easy super-jump-ring to aim Chargers at, and the Kraken is great for staying alive on the Tower and discouraging potential boarders; it's usable, and I like using it.
For Rainmaker, the Vanilla Inkbrush's speed lets it reach the Rainmaker faster than the other team, and it can shatter the Rainmaker's shield easily by planting a Sprinkler just outside of it; when it's overlapped by the shield, it doesn't get destroyed and keeps shooting into it, letting you passively help break the shield, and Inkstrikes let you shield-break from a long distance or impede the Rainmaker's progress while the enemy has it, and though it once again struggles in direct combat, it might be passable for attacking the Rainmaker carrier, since they cannot shoot their one-shot mega-inknado very quickly; it's certainly an alright pick, in my opinion. The Inkbrush Nouveau suffers in this mode, as its only real strength here is Bubbler-passing and attacking the Rainmakef carrier, or carrying the Rainmaker itself; otherwise, its speed doesn't matter since it can't pop the shield quickly and Ink Mines will be detonated by Rainmaker inknados long before they would be in the blast radius, making them mildly annoying at best; I wouldn't recommend it, but I'm sure it's usable. The Octobrush shouldn't go for the Rainmaker at the start of the match; instead, it should go around placing Beakons for its teammates, inking a path for them to use when they get the Rainmaker and charging Kraken for if the other team gets the Rainmaker (or to ink a path for your team's Rainmaker while simultaneously assaulting the enemy team, making them retreat or get splatted), and you can always double back if the enemy team gets the Rainmaker, and you can perform pretty well in attacking the Rainmaker carrier and anyone guarding them, though you still shouldn't go for open combat if you don't have to; it's in more of a support role, but he Octobrush can pull its weight here.
TLDR: Inkbrush works best in Turf War, but is okay for Splat Zones and Rainmaker. Inkbrush Nouveau is serviceable in Tower Control and Splat Zones, but I can't see a reason to pick it elsewhere. Octobrush is pretty good in all modes, but faces competition from the Krak-On Splat Roller in terms of its role on a team (support, but with some firepower). At least, that's what I think.
So, is any of that correct? I only use the Octobrush seriously, pull out the Inkbrush on occasion, and loathe the Inkbrush Nouveau, so I'm not entirely sure if I'm right about that.
No, octobrush is amazing.
Ah, why exactly? I mean, I like it too and I think it's pretty good, but I wouldn't call it amazing.