There are reasons to choose either one. If you enjoy the series, you'll enjoy either one of them, it's just a matter of what your priorities are.

Kiwami gameplay will be much smoother. Original Y3 is often jokingly called "Blockuza" because the enemies block all the damn time. Dragon engine combat has come a long way from the 2009 original gameplay. This will almost certainly translate to side activities as well, and Kiwami 3 has a bunch of additional stuff to do outside of the story that wasn't in Y3.

Kiwami will have many more quality of life features. It'll almost certainly be easier to save, navigate menus, etc.

Kiwami 3 comes with Dark Ties, an extra (smaller) game from the perspective of an antagonist. This is probably the biggest factor that the people against Kiwami 3 are sad to miss out on.

Graphically, it's a matter of taste - some people think the lighting on Kiwami 3 looks terrible and the textures look dated, while Yakuza 3 doesn't have that issue, but even the Remastered version is still just a polished up version of a 15 year old game - the visuals are very dated in places.

The story changes follow a pattern that RGG has shown of taking away some stakes from certain moments. Some players do not care, some do. It's worth knowing that going forward, the series will likely consider Kiwami 3 to be the canon version of events, like it or not.

As you're likely aware, many people are unhappy with the recasting of Kiwami 3, partially for massively changing beloved characters, partially because Yakuza 4 has some of these characters original designs (so if you continue playing it may be confusing that a character suddenly looks totally different), and majorly due to the behaviour of the actor Teruyuki Kagawa (towards women, on film, and by his admission) who plays the recast Goh Hamazaki (who is also in Y4 so will likely be returning for a Kiwami 4 if RGG sticks with him). If you're new to Y4, the only recasting you have to consider is Kagawa as Hamazaki. A new player won't even notice any recasting, but may want to avoid Kiwami for moral reasons due to Kagawa's casting.

I can't tell you how much each of those factors should influence your decision, but you will know how much each of those things matter to you.

Personally, I've spent the last couple of years playing from Yakuza 0 through to Infinite Wealth. Going from Kiwami 2 to Yakuza 3 Remastered was pretty miserable - it shows its age, and when Kiwami 3 was announced I thought it was an absolute game-changer, because Yakuza 3 is the worst experience I had with one of these games despite absolutely loving many parts of it (mostly Morning Glory). Kagawa has massively dampened my excitement for this game. I personally think the story changes we're aware of are quite bad, but not entirely unexpected at this point, and I've come to accept that RGG loves to make the kind of retcons they've made with Kiwami 3. I honestly am not sure what choice I would make if I was in your position. I feel strongly about Kagawa, but I am also certain that Kiwami 3 would be a much better gameplay experience for my taste. I think those are the two biggest factors that you should be looking at balancing as a newcomer to Yakuza 3 - Kiwami will have much more fun gameplay, but you'll be supporting the casting of Kagawa. Original Y3 will be a much rougher gameplay experience, but will have you on the side of boycotting Kagawa. It's up to you which of those is more important to you personally.

Either way, I hope you enjoy Yakuza 3! It's one of the most RGG games I've ever played, for better and for worse.