Good question. Let's address each of these separately, as they are very different things.
Private or dedicated tables is a result of casino like Royal Panda and software provider like Evolution Gaming agreeing that they should provide players an enhanced playing experience.
In this case Royal Panda have a private blackjack and roulette tables only for their customers. They still use Evolution Gaming's infrastructure and dealers to offer these, but only customers of theirs will see them in the lobby.
This lets them organize special promotions, choose the look and feel of their tables and even make sure the outfits of the dealers align with their brand strategy. It's these little things that can improve your playing experience by a lot.
Native live dealer tables, on the other hand, are offered by the software provider to all their clients (being the live casinos in this case).
The big advantage of these is that the dealers are fluent in more than just English, and in most cases are native speakers of another language.
Popular native tables include Danish, Turkish, Spanish, Italian, French, Russian, Polish and German. Though there are others being introduced as live dealer technology is getting more and more mainstream. Just recently we saw Flemish live roulette being offered at partners of Evolution Gaming.
A great selection of these is available at Unibet Casino who also happen to offer some impressively high betting limits.