I was in a private school before I came to Australia, because public education from where I cam was trash, however have been in a public school when I started school here, which was at age 5, started school overseas at age 3.
Both are similar, however one requires you to pay a heavy fee for what you can earn for free. It's good if there's no good public school around you, if there is however, Public education should be the number one option.
Private might be good for the disclipine, etc... but even then I've seen many idiots from both sides of school.
tl;dr Go to which ever you like, both are fine, it comes down to the individual in the end.