I'm sure this brilliant BYAP thread has already done the rounds here, but the issue they tested for keeps popping up.
In this 2010 trial from Australia, they compared a variety of types of veggies grown in three systems, identical except for the method of supplying water:
The result from this small 18 month trial is that timed flood-drain wins, hands down, across most plant types with faster plant growth, more worms, and larger fish. It also used less energy since the pump switched on and off.
The constant-flood and bell siphon systems traded back and forth for 2nd place. In the end, certain kinds of plants did better in constant flood and others with the siphon.
They provided no explanations for why they thought the results were what they were, though others made a lot of speculations across the 40-page thread. They were trying to be un-biased, so avoided making judgments.
One of the most interesting findings, to me, was that the systems all tracked along a consistent temperature profile. I would have suspected that the flood and drain would have been cooler due to more evaporation, but it didn't happen that way. This might have implications for cold weather.
The fact that constant flood and siphon systems did just as well as each-other in growth makes me think that constant flood would have the edge over siphon, since you don't need a sump tank. On the other hand, it did produce a lot of slugs.
Flood-drain with an indexing valve wouldn't need a sump tank either.
I've attached some pictures of the final growth, though this is after 18 months of crop rotation and harvesting. There are many more pictures, detailed figures, and helpful comments on the thread. It's an education.