Glad you posted - Thankfully, I remembered, too.
Seagrasses are true grasses that grow completely submerged or tidally exposed in marine water. They are vascular plants. Algae are barely plants <gg> and do not have the "advanced" features (sea that chapter for description).
Your question is a good one. As far as I know, there are no data to compare uptake, and relatively few on uptake of the sort that aquarists are interested. The ecology of seagrasses is fairly well studied, but lots to go. In the wild, where there are seagrasses near reefs, the communties are capable of removing all the excess production of the reef...and absorb all the terrestrial inputs, too - at least normally (they may be buried where activities on land have caused above average deposits to flood the coastal areas). As a community, they appear, like reefs, to be nutrient limited. Conversely, the higher than average plankton in seagrass areas and the amount of detritus they produce feeds the reefs. A sort of mutual backscratch. But, it is not just the seagrasses. Also, like the reef, its the whole community, and the blades of seagrasses trap particulate matter and allow it to settle in their dense rhizome network. here, with all that "food" are a myriad of organisms - from very high sponge and mollusc population, to predators, brooderies, etc. Because there is so much nutrient waste trapped, it is well broken down and mixed and sediments are usually silty to mucky - and they stink!! Why? because there is a very very high level of microbial (bacterial and other) action going on - and it is probably this aspect that allows for the nutrient efficiency, rather than the seagrasses, per se. However, without those grasses and the communtiies they foster, you have a regular sandy bottom that is, by comparison, rather useless.
Algae may also grow across sandy bottoms or directly on hard substrate. They do not form the intricate ecological communities to the same degree (exceptions occur, like kelp forests, etc.). More more often than not when on reefs , macroalgae often are symptomatic of a reef receiving too much nutrient and this is called eutrophication. They react very quickly, too. Now, of the algae, the turf species that grow intertidally seem to be the most efficient. They are highly grazed and have the fastest growth rate increase. Among these are aquarists undesirable filmaentous species, as well as very attractive astroturf-like types. The macroalgae, in general, are probably much less efficient at nutrient uptake roles in the wild. Phytoplankton and bacteria just respond so much quicker and usually deal with the problem unless it is chronic...and then the slower macroalgae respond. i have seen some references suggesting that corals, sponges maybe too, are more efficient than certain macroalgae at nutrient uptake. Makes sense, too.
So, if I were to wager a semi-educated guess, seagrasses probably have among the slower growth rates, followed my macroalgae, then filamentous then other turfs....and this would be a decent measure of their nutrient uptake ability, too. However, as a community, seagrasses and associated microbes are probably the greatest. They also are normal with healthy coral reefs and have that "symbiotic community" aspect that I think is desirable.
So, if you plant a few seagrasses around your refugium, are you going to "filter" your water? No. Same with mangroves....same with macroalgae, I suspect. But, they will all help. If you have a seagrass community with good sediments and of good size, it will probably contribute significantly to nutrient processing.
How's that?
Eric
