The core book has rules for simple success rolls, where you can't fail, the roll simply determines how good you did, either doing great, or bad enough to, for example succeed but take some extra time to do so. And Margin of success works differently, in the Quickie to get a margin of success of 20, under a goal of 50, you need to roll less than 30(so Mos is based on how much under the goal you rolled), in the core rules the roll wound have to be twenty or higher, and under the Target number.(The MoS is how high you rolled while still being under). The core also has rules for Excellent Successes, while I believe the quick start does not. the core also is more detailed on what stats belong to an ego, and what belongs to the morph. Differences in networking rolls, and differences in hacking(very slight or simplified I believe). On a whole things are fairly similar except as noted above, I think combat and action plays out similarly. Most of the differences seem to be in how simple it is made, or explained.