We replaced our carpets with hardwood floors and when we built on 3 extra rooms, we left the floor concrete and we stained it. This was all before we got Rexy and Rowdy. BUT my mom (who lives with me) has carpet in her two rooms and I had a devil of a time with Rexy when he was potty training. He NEVER went on the wood or concrete but he would make a bee line for her rooms and potty there on the carpet. I finally had to put down a very hard bamboo type rug cover in the hall with carpet, and had her keep her doors to her rooms shut until he got out of the habit and now he never goes in the house anywhere.
Rowdy on the other hand marks
but it is just a sprinkle here and there, on the rug, concrete, or wood, makes no difference to him.
You will find a couple of threads on this subject if you do a search. I would NEVER have anything but wood or concrete (or tile - there's a good discussion of the virtues of tile too), EVER AGAIN. We put down the wood floors ourselves a few years ago and thus, we pulled up the carpet ourselves. OMG!!!
It was just totally gross, disgusting, and horrible to see all the stuff in and under the carpet. I almost died and vowed never ever again to have carpet in my house. I heard someone compare carpet to wearing a sweater for 10 years without taking it off and then just washing off the outside of it while wearing it - because shampooing the carpet is only getting the dirt off on the surface. Anyway, pulling up our carpet made a believer out of me!
I think it was txshopper who posted some great pictures of her concrete floors after they took up the carpets and stained the concrete. They were beautiful. We love ours too.
If I remember correctly on the threads about hardwood vs laminate was that you have to be pretty careful with laminate as it will warp or peel - if it gets wet. Of course, that could be the quality of the laminate and I am sure there are some good ones. We have an occasional spill or throwup on the wood, that I don't find till they are dried sometimes, and we have had no stains or warps or any problems at all.
Good luck with your decision!