1. Instead of Fort, Will, and Ref saves, you've got Fort, Will, and Ref Defenses. In SWSE, they're 10+character level+ability modifier+class modifier (most base classes give a +2 to one defense and a +1 to another)
2. When you use the kinds of attacks that would generally require a saving throw in D&D, you make an attack roll against one of the targets defenses, or, in some cases, a skill check. So if you want to use the famous Jedi Mind Trick (assuming you have that Force Power available) you make a Use the Force check against the target's Will Defense. However, because Jabba is pretty high level and Hutts have a species bonus to Will Defense against Force powers, it's pretty hard for Luke to Mind Trick Jabba.
The biggest advatages to 'flipping' saves are...
1. It makes resolving area and other multi-target attacks (in SWSE, you're basically thinking grenades, autofire, and some Force powers) somewhat faster, because you only have to roll one attack roll and then compare it to everyone's defenses.
2. It makes the game a bit more consistent; the attacker always rolls.
3. In SWSE, they've eliminated a standalone 'defense' (aka AC in D&D land) in favor of ref defense; this elminates a bit of weirdness in D&D (where some spells had touch attacks and other rather similar spells had ref saves).
The biggest disadvantages are really psychological; it's tough to not be able to do anything but hope the bad guy rolls low when he's tossing Force Lightning at you. And it means that when you fireball a horde of identical mooks, they'll either all succeed or all fail.