I have this problem. My ISP isn't displaying all the messages that I see in Google, and I cannot apply to someone who lists hs address as snipped-for-privacy@null.com. Please bear with me. I'm trying to reply to the last message by the above poster.
The reason the two scenarios are not equivalent is that, during operation, the unused propellant (in this case water) must be accelerated. Thus, when the water is half expended, the other half is moving at the same speed as the rest of the rocket. That's not a big deal if the propellant mass is small compared to the rocket mass, but in this case, even the unused water at the halfway mark may be several times the dead mass. That's a lot of kinetic energy put into the propellant that you don't get back when you expend it. There is also the potential energy of lifting that propellant.
(Actually, you can get some of the kinetic energy back by retaining some of the the mass and allowing its associated energy to work against drag. If you were very clever, you could expend it after it did this.)
This is not just a problem with water rockets. It's the reason that low Ve solid propellants are used primarily in boosters. Certainly, if you have an upper stage with a given impulse, you want a lightwaeight propellant with a high Ve, rather than a heavy propellant with a low Ve. After all, you have to lift that propellant before you burn it. Well... it dosn't really matter if the propellant is in a segregated stage.
Hope that helps.
-Larry Curcio