We had engineered wood in the bedrooms of our old house and I much prefer it to the carpet we have now as it is easier to keep clean and doesn't harbour dust and dust mites. I don't think it is that easy to damage and I think if your DC were going to damage it then they would damage it downstairs too.
I would go for carpets myself, as we find they make a terrific difference regarding noise and draughts. We were previously in a bedroom with carpet and after redecoration moved to one with floorboards and rugs. It looks terribly terribly elegant, but believe me, I am definitely putting carpet in when things allow.
But then my DH cannons round the house like a one-man elephant herd.
I think it is down to personal preference. We have oak downstairs and it is marked up from kids dragging toys all over. We have carpet upstairs and they do pee on it (no sick yet, but I'm sure we'll have that too). I'm more of a wooden floor type person - I like to change it up with new rugs every now and again. We'll soon be replacing flooring upstairs and I'm thinking we'll sand the floorboards in the kids' rooms, but DH wants carpet in ours (also for noise insulation as above the kitchen). I'll get the kids patterned rugs of some sort which can be cleaned and will hide stains. I wouldn't put expensive carpet in the kids' rooms though as it will need replacing.
We are having oak flooring on the ground floor (apart from kitchen which will be tiled). But can't decide what's best for our bedrooms carpet or oak? the staircase is oak as will the floor on the landing.
DP wants carpets, he thinks DCs will ruin oak by dragging toys around etc, but I think they will ruin carpets by being sick and peeing on them! They are 5 and 3 and we have another on the way. Carpet is also cheaper.