I was lucky enough to do one of the private reseveres in Kruger National Park, maybe 8-9 years ago. We stayed for 3-4 nights and do two drives a day. While technically you could say both Kruger and AK are safaris, it was night and day different. Hands down the best vacation experience I have ever had, and counting down the days till my kids are old enough to go (place we stayed requires everyone to be 11 and up I think).
You truly feel you are one wild, because you are. Open air jeeps that hold maybe a dozen people, although we never had more than 6. You get so close to the animals, never know what you are going to come across, and even the 5am wake up calls were not that bad. We were also lucky enough to stay at a really nice resort, so even the downtimes between drives were amazing.
I love AK, but it could not even compare to what we were able to do.