Cup shocks are slightly firmer which means that they offer slightly more roll inertia, but ultimately the amount of roll resistance that determines where the car settles during a bend is down to the firmness of the springs and the ARB.
A set of cup shocks is very cheap and at least then they are new, where as your current ones quite possibly are past their best.
Add some eibach springs and it makes a big difference to how much it leans, and the extra roll resistance makes it feel a lot more sure footed on turn in, but dont be seduced by that side of it, it can make you keep going harder and harder until your corner speed actually drops but it still feels so epic on turn-in you think you are improving it.
A bit of compliance is very useful IMHO, especially if you like to hop the occasional kerb on track, so dont search for a setup that allows the car to corner totally flat IME