Lakwhut, because the OU and Stark K only certify glatt meat, that has become the basic standard in the US. The Rabanut also certifies non-glatt meat. There are other kulas that the Rabanut relies on that aren’t widley relied upon in the US.
On the other hand, there are kulas that are relied upon in America which aren’t accepted in Israel. For example, even the worst Rabanut is machmir for Yoshon (even for things produced out of Israel).
That’s why many Israelis won’t even think about touching anything with an OU on it (I heard some Israeli Rabanim say better to eat Rabanut than OU).
Basically, it all depends on the kulas that you are used to reliying on as opposed to what you aren’t used to relying on…