Our new car came with installation of a catshield. When talking to various autobody places, they were skeptical it would matter because if they'd cut out the catalytic converter, they could just cut out the shield. It would be nice to see if they had data on this, but I haven't seen any (I even asked our insurance agency if they knew of any analyses on it but they said they didn't).
If you use stainless or something it will really piss them off. Aluminum will deform, frustrating cutting attempts. Mesh will block access just as easily, maybe go for a stainless mesh so its really annoying to cut through and bank the weight reduction/cooling benefits.
If you use a grinder, the abrasion will take a lot longer as you have to clear both spots where you would like to cut.
If you use a sawzall aka reciprocating saw, the blade has to have totally clear movements or else it will flex and slow down.
If you use a torch it goes quicker, but the set up and hauling the tanks is not easy, torches are fiddly, especially if not properly maintained, the smoke is poison, and theres fuel lines down there to boot.
Unpleasant. They'll just curse and roll onto the next mark.
Also hybrids are more targeted for cat theft because they have more of the metals than normal cars to compensate for frequent engine stops and starts from cold.