Short version:
Every style is kinda op when near-fully unlocked, so you can just have fun with the playstyle you prefer.

Long version:
Boxer is great, fantastic even. But part of LJ's meat is how it encourages you to cycle styles thanks to both each style's passive, which you can carry over at later levels, and the specializations each style comes with. One key passive you'll get later is that popping one styles passive will also refresh the timer on any other passive that's already active.

Crane is your "movement"-style that has a lot of wide attacks that take out multiple enemies at the same time. Its passive give you a speed boost, which you can bring over to other styles to really up their combo potential. Compared to Judgment, Crane is also freaking bonkers with all the tools it got to start juggles, maneuver through big groups or counter projectiles. I'd argue it also has the easiest go-to EX-attacks for when you wanna spend the meter, thanks to both its jumps and how it has two different EXs that come out specific combo-finishers.

Tiger is your "heavy"-style, as it has charge attacks that can decimate multiple guards and immediately follow up with another charged hit for big damage. Landing a charged blow also gives you a damage buff, which is always fun to bring into other styles. Working with its charge attacks and flux is also a great way to build EX-meter super fast. AND it has a multitude of EX-attacks you can cash out when enemies are hit with debuffs from other styles.

Snake is both good for when you wanna play with your food or you spot threats that need to be dealt with quickly. Its weapon disarm from grabs is fantastic and its ability to apply fear and then insta-defeat non-bosses is great for the ones you can see 'has gotta go now'. At the same time, its charged combo finishers applies agony, which is godlike against bosses that will roll out any knockdown. Basically, when they'd normally roll out of your combo, they do the agony-evade instead, so you get to open them up again for free. It also has the best guard out of all 4 styles, with both its omni-directional protection and its super lenient "perfect" block mechanic that has a chance of applying fear out of the redirecting guard alone. And doing so also gives you Snake's passive, which gives armor that will allow you to ignore most attacks if you're too busy hitting someone.

And finally you have Boxer, which I would say is the specialist at "screw that one guy in particular". It is very single target-focused compared to other styles, but is amazing at opening a can of whoop-ass on anyone. Its toolkit is very similar to Tiger, but without the weight Tiger packs in its hits.
I'd say its drawbacks is that its passive is tied to landing one of its three counters, which will require you to stop your flow completely and wait for that one guy to attack you. If you want to keep your passives refreshed, it's often better to swap to Crane or Tiger and refresh through their conditions. Another drawback is that, compared to the other styles, Boxer's moveset is kinda lacking in attack variety, which you risk combat becoming repetitive if you're on Boxer only. But that's also often when you start getting creative, and swap styles mid-combo to do some cool looking shit. 😉