The advantage in parlays is that you increase your ROI over straight bets when you can consistently pick winners (conversely if you are a losing player, parlays make your ROI more negative, so be careful).
RR parlays maximize the advantage you have using parlays, at the expense of a large increase in variance.
parlays generally give slightly less than the correct odds for taking the winnings from one and applying the sum to the next bet (not true in all cases, many books give full odds on 2-team parlays), so action-reverses which actually give the full odds should have a higher return, also the action-reverses allow you to get down twice as much money as a round-robin if you're running into betting limits, which seems to be the primary reason to use round-robins in the first place (assuming the limit is on base wager amount, rather than maximum possible loss, not really sure what most books go by)