Do rabbits have the same or similar intelligence to dogs and cats?

No, they have a limited IQ, but they can be trained to be potty trained...until they get to a certain age then they start pooping and peeing when ever, where ever they please, also most rabbit owners don't know that rabbits have to be neutered as well...if a rabbit is not neutered then they spray there territory...I also notice that if a rabbit is close to its owner the rabbit will greet you and give the same unconditional love other pets give...rabbits does follow its owner from room to room, they also show emotion such as temper.