You probably know the size of the tires will make a significant difference in the attributes you're looking for. If your GPs are wider than your R3s, there will be a difference in traction, puncture resistance and rolling resistance.
Another big consideration is if you are running a tube or not. If you are tubeless, both the 5000 and the R3 come in a 32mm size. I find the product lineup on Vittoria's website is confusing: online vendors list a "G2.0" while Vittoria only show a "Corsa" in their lineup. Assuming these are both the same, the Vittoria only comes tubeless in a 28mm. It will ride significantly differently than a 32mm, which will have better traction and fewer pinch flats, and many will contend lower rolling resistance (that's complicated). If your plan to continue to use a tube, you've probably seen you can get the Corsa in a 32mm.
Sounds like you've read other info about tread. Cars have tread to move water away due to a phenomenon called "hydroplaning" in which the car floats on the water. Bicycles do not go fast enough to hydroplane, so tread does not provide any benefit. If anything, it's probably worse. However, it does help with debris, though I'd be skeptical that the narrow tread of the Corsa provides any benefit. I have a bike with Grand Bois Hetres and I've noticed no traction benefit over my previous Gravelking or Pari-moto slicks.
There is a site called BicycleRollingResistance.com (BRR) which tests the rolling resistance and puncture resistance for many models of tires. The tester was disappointed in the tubeless G+ 2.0 and in their tests it was almost 4w slower than the tubeless GP5000 in the same size and inflation. The Continentual in it's tubeless configuration is the 4th fastest tire they've ever tested (all tests are conducted with a tube; butyl, I believe).
While I personally have not ridden the Corsa, I have ridden other Vittoria tires. My bike (recently stolen, sad face) was a Look 585 on which I ran Vittora Corsa Speed tires with latex tubes. They are the fastest tire ever tested by BRR and I found them to be a sublime revelation. I don't know if I was faster (though all my fastest Strava times were aboard them) but they ran incredibly quietly and smoothly.
I also recently had a chance to do a few test rides that had Vittoria Corsa Controls, in 30mm. They are a teeny bit heavier than the G2.0s, and about 1W slower according to BRR. I first rode a Cervelo R5/Reserve 50 and then an Open Min.d/Enve 3.4. Both were running the Corsa Controls. I was slow on the R5 and the ride was rough. I was fast on the Open Min.d and the ride was smooth. So in this case, the frames/wheels overwhelmed the effect of the tire, though often the opposite is the case. My point being that the Corsa G2.0 will not be so outlandishly bad or good that it will make/break a nice ride on a nice bike :)
I personally am considering the GP5000s or a Schwalbe Pro One TT. The latter is very fast according to BRR and I like that Schwalbe has a tire recycling program. However, the Schwalbe is only available in a 28mm so I may very well opt for the GP5000 to get a larger carcass.