Ganondorf is a sword user mainly(he's never actually used another weapon outright in canon. Magic not counting. Though he does have a Knife that went unused).
Pig Ganon is a Trident user mainly. He clearly didn't have access to his Trident yet anyway, hence using two Swords in OOT, the birth of this form. He's still tied to the Gerudo so the form directly takes from his core abilities at the time.
There's no reason he'd suddenly pick up the Trident when his Gerudo heritage trained him as a core Sword User(Ganondorf clearly cares about his heritage a lot more than people credit for. There's a good reason he directly went double blades in WW. Meanwhile, Puppet Ganon is just something of an afterthought. He doesn't really take to that form and even denounces the idea of destiny at the end of the game. Demise's influence was lifted for him by then, or is at least heavily implied to be the case). Pig Ganon gained the Trident only one time via the story in one of the many branching timelines. It's unclear when he even got his Trident for ALTTP, and it has no ties to FSA. Probably just the same place held it, but it's completely offscreen.
Just cause they're the same person doesn't mean the forms fight actually the same in any constant motion. They're very different characters in function. Hell, there's multiple Pig Ganons who work entirely differently. Bipedal Ganon is a weapon/magic user(which the blight Ganons are directly based upon, but also a loose take on Phantom Ganon), while his more boar-like forms are brutish animals who don't use weapons but sometimes a bit of magical ability.
Overall, they're separated heavily in canon and it makes sense. Ganondorf prefers Swords. Pig Ganon prefers Tridents. They don't even use mainly the same abilities beyond, what, teleportation? At most? Ganon doesn't even float either. That's a Ganondorf thing. You could also say they're both physical powerhouses, but it's different too. Ganon only uses that in a defensive manner, usually bodychecking Link or being able to do his Trident(and one-off Sword) swings, while Ganondorf actually will physically punch and kick from time to time, while also using magic and swords.
On another note, his new design is the most fitting for his current moveset. His new Sword is actually a huge sword, not a thin kitana, and thus, works best with heavy swings. His bodyshape isn't much different, and he's also designed in a way where he is easy to work with brute force. He's basically the epitome of Smash Ganondorf, but in a canon game, design-wise. It's only a matter if the animations even work fine, otherwise they wouldn't use this one. You ain't getting a super moveset overhaul like that. Falcondorf is here to stay. If you want a new Ganon/dorf design, wait for a new character slot. Maybe we'll get one, but I doubt it.
Fixed so it's a bit more clear(though obviously if I say Ganondorf and Ganon separately, it's kind of obvious I mean a different form, but... people try to conflate them as being more connected than they are. Paying quite a bit of attention shows that they're so damn different it hurts. They could easily retcon it to being two different people sharing one body and it'd make a ton of sense. Especially now that Pig Ganon is effectively far more brutish and less of a tactical master that Ganondorf is. They have separated them to some degree besides abilities, but yeah).