Demarree involves separating the queen from ALL the brood leaving her in the bottom box with nothing but drawn comb and/or foundation so splitting a double brood isn't really a Demarree, there are numerous advantages of Demarree - in it's purest form you don't need to inspect the bottom box for a few weeks, and only the top box until all the brood is sealed, however be aware that this way you end up with a deep super. 'Rolling' it is a bit more work but essential with a really prolific queen, but you still have to decide what to do with the top box towards the end of the season.
Another advantage (to some) is that you go into winter on a single brood again.
It's also a good way of working out your older brood frames. I have three stacks of brood boxes full of drawn frames at the moment. In the spring, the newer (many 'virgin comb') cleanest frames will get used for the new season's Demarree's whilst the older, mankier stuff will get scrapped.
Don't be fooled, bees will swarm on a double brood, and then you will have more kit to muck around with to sort it.