Private reserves use networks of tracks through the bush, rather than the tar roads which form a major part of your public Kruger experience. They go to places you are not allowed to enter by yourself. Guides know their local patch intimately; you will find it difficult to keep up with where they are taking you without their feel for the bush. And you can get off the vehicle to follow up on sightings and look at things of interest, rather than being stuck in your car.
In the public Kruger, unless the animals choose to approach the noisy and dusty roads, you can’t see them.
In private reserves, you drive on and off road. You can go looking for animals. Importantly, once you have located animals, you can follow them. Trails are laid out cleverly to enable access to much of the traversing area without discomfort. You will be able to observe animals pursuing their normal activities rather than snatching glimpses of them as they pass by.
Decent track networks, and being able to ignore them completely, substantially increases your chance of outstanding sightings, and enhances their quality when you have tracked them down.
This may seem obvious but it makes a huge difference – private lodges use specialised vehicles to go off road and really work the terrain. They go to places you could not reach in your own vehicle.
Big cat sightings are a particular speciality in some areas like the Sabi Sand. Leopards are frequently seen. You would need to spend weeks on the tourist drags of the public Kruger to get lucky. Here they are largely habituated to the presence of a few, unthreatening, vehicles, and carry on as if they were not there. The intensity and duration of these sightings is completely unlike the fleeting, crowded glimpses of the public park.