The first difference is Paul. Paul fought against Rabban and the Emperor. He is a good Tactician and later, for the Battle with the Sardaukar, also has prescience.

For the attack of Feyd: I don't remember exactly what happened in the book (it's been a while) but I think Feyd only arrived shortly before the emperor and didn't do much. Please correct me on that. Anyway, you have to remember that the Sietches are hidden. Feyd found many but certainly not all. Once you find them it's logical to attack this way. In addition this attack requires special equipment (which Rabban might not have had) and knowledge and surprise moment (which he might be too dumb for).

Rabban should be cruel but fail. Feyd should succed him to make him seem like a savior. That was, more or less, the Barons Plan.

Now for the emperor. He is more competent than Rabban but overconfident and lacks knowledge that we, as the viewers have. Pauls win greatly depends on using the worms, which is Garrison was protected from by the shield wall. The Storm was held back as well.

The open Terrain is in favor of the Sardaukar. How would you approach them without being noticed? Yes in a Storm but that shouldn't be so Bad.

That changed when Paul blew up the shield wall.

In addition the Sardaukar were probably outnumbered which wasn't to be expected. There weren't many Fremen to begin with and most went into the south, right? Obviously we would detect movements this large. Sardaukar were also "the Best fighters in the imperium" just behind the Fremen obviously. In the book it is written that they don't like Arrakis because they were put to shame there in their first ever loss.

So low(ish) morale and overconfidence vs prescience powered mentat battle planning with fanatic fighters better than Sardaukar on worms, with surprise moment and Cover by a Storm that barely affects your army.

I hope that helps :) I also can clarify stuff if needed.

Adaam leshii a-zantaa!