Comparison versus RAM models
You can defiintely cook up promise problems where RAM is much stronger.  Of course it's weird because you have to actually phrase your problems in terms of comparisons. suppose your memory is initialised into a permtuation, i.e. with memory registers x(1), ..., x(n) taking on the values 1, .., n exactly once each.    The problem is to compute the # of i s.t. x(i) &lt; x(1).