I have seen more 4 wheeled "cabin" bags being stopped than 2 wheeled and no wheeled. One specific type of bag can be difficult despite the fact that they are designed for the overhead bins...the Truckie child's wheeled case due to their sometimes awkward shapes.
I have not had a problem with the bag that I use, but more than once it has gone into the wardrobe/cupboard at the front of the aircraft cabin a few times due to other pax filling the overhead bins. Eventually I started to ask if I could stow my bag in the cupboard since it is so much easier to retrieve when getting off the plane than fumbling about in the overhead trying to free it amongst the duty free booze bottles from the other pax.