You have to bring them up slow on flat top electric and induction. If you bring them up slowly, they won't warp.
So what you need to do is get you a 2x4 and a hammer/mallet. Toss the pan in the oven at about 250 and let it get nice and hot. Get your gloves or oven mitt on and take the pan outside. Put it on a flat surface (like a wooden picnic table (or even the ground) upside-down. put that 2x4 across the bottom lengthwise (short side down) and move it across the bottom of the pan while you whack it with the hammer/mallet. You should be able to see from how the 2x4 makes contact with the pan whether it is still warped outward. I did this with my 11 7/8" Matfer-Bourgeat and got it back to flat without too much trouble.
So as for what is less likely to warp? Well, as long as you bring it up to temp slowly, it shouldn't warp. But as far as thick pans, I think Matfer Bourgeat is 2.5 mm thick. De Buyer's larger pans are 3 mm thick, but their smaller ones are 2.5 mm. Those are the two brands I have (four in all; two of each). The only one I ever had an issue with was the larger M/B because I blasted it with heat right out of the gate with my induction cooktop. I think both M/B and De Buyer now have a slight upward bow on the base of their pans to help avoid warping. But if you bring them up slow, they'll be fine no matter the thickness or design.