Under-eye fat repositioning at a private clinic?

I’m planning to get under-eye fat repositioning, and I’m looking at places like Shinshael, Oskin, Objet, Saegim, Roy? I’m checking out all the decent places, but should I look into private clinics a bit more? I heard these days a lot of people who don’t like factory-style clinics go to private clinics, and I feel like there might be a reason for that, so I kind of want to visit about 3 private clinics and then go to larger clinics for the rest