I saw a question about this on here awhile back, and can't find it again to answer, so I though I would start a forum about my experience so far to help answer the question. Keep in mind my system is in a ten gallon aquarium, the water is pumped to the bottom of 1 main filter and 2 aux filters. The main filter gathers a bunch of the solid waste (lava rock is the media in all filters) The water go up through the rock, past the plant roots, and spills back into the tank. The 2 aux filters work the same, but with a slower flow, I have those in mainly for growing more bacteria. Plant roots are completely submerged all the time (so I guess that's akin to a constant flood system) Tank completed cycling recently, and has remained stable and healthy since increasing fish load and feeding. Currently living the tank are 3 feeder goldfish, 4 fancy guppies, 4 cherry shrimp, and 2 yellow shrimp. Not to mention an abundance of 2 snail varities (which are helping to keep main filter clean), some worms, and 2 very small slugs. The tank stays between 76 - 80 degrees.
The plants I'm having success with so far are:
Ficus tree - loves the system! Is actually the centerpiece and largest plant of my system. It was just cured of a spider mite problem (I took it from a friend) when I put it in with the other plant that started the system, a schefflerra, and had about an inch of new growth from week 2 until now.
Schefflerra - was having a similar spider mite issue that I cured it of before I put it in. It was alive, but hadn't grown a new leaf in months. It has sprouted threw new fronds and has new shoot growing since starting.
Creeping Fig - another member of the ficus family. I have two types that were cuttings, very small, when I put them in. The one has a new shoot growing out of it and the other has some amazing root development on it. These were added just a few weeks ago.
Ivy - I have several types in my system. All rooted very fast and have new growth.
Moss - I have several types, though I'm not actually sure what all of them are. The one is the common moss you'll find growing in a carnivorous planted tank (I actually transplanted it from my carny tank) and it's doing well. The other looks like a cross between a common carpet moss and java moss - dense & thick, green & very pretty. It has started to do well to - the main clumps are sending out thin lines of growth to neighboring rocks & exposed roots.
Tarantula Fern - just put it in and is sitting in a crevice on the ficus roots that are above the water line, but are drawing up moisture through capillary action. I checked it a few days ago and there is root development from the rhizome, and the leaf on it is very green, though no new growth yet.
Club Moss - I can't tell yet with this plant. It grows well in very moist places (it loves my carny tank and grows by sending roots down to the soil, but all the leaves grow above the soil, lifted up by the roots) some parts of this plant seem to have finally established and are doing well, other parts are rotting. I can't figure out what the difference in placement is yet.
Philodendron - as long as it roots, they are very happy. Though I have noticed some cuttings are taking way longer to root, and some rooted after a day. I don't know why. I have two that have new growth on them.
Dieffenbachia - had it in a vase of water before, no growth in months. It has gone crazy with root & leaf growth. Huge leaves, great coloring, and roots shooting straight down into the gravel from the top of the tank. Both stalks have new stalks bursting from the sides.
Zygocactus (christmas cactus) - added some cuttings about a week ago. new root development and new shoots forming.
Cerpigia Woodi (string of hearts) - rooted quickly, and has new growth, though light levels may be a problem because new leaves are very tiny. Recently upped my lighting, so we'll see how that changes things.
Java moss - alive and doing well, though not the kind of growth I've read about in other forums, this is my first time growing it.
Elodea - just planted in my tank the other day, but seems happy so far, no rotting on either root or top ends.
I plan on adding some seeds from a purple velvet plant soon to see how seedlings do in this kind of set up - all this learning is going to be put to use in the spring for an indoor veggie set up with a 55 gallon tank. I hope this answers some questions for those starting out or wondering about house plant functionality in an AP system.