If you are careful and maintain good nutrients in the water column, generally there is no difference for most plants.
Simply having large roots does in no way suggest they prefer root uptake. These plants come from high flow regions such as streams and rivers that get scoured.
They need them to hang on and as well as when the water level goes down and they are exposed to air(no water nutrient sources available them!). So they have a ecological plan there, not a static environment......
I grow massive Crypts and sword plants without any sediment sources, they become very weedy. I suppose I could do a controlled study and take the before/after dry weights, but Cedergreen, Madsen 2002 already did this experiment for 4 weedy submersed aquatic plants, Crypts and swords are not really permanent submersed species in nature, thus are poor candidates for such generalizations.
Cedergreen and Madsen found even cutting the roots off had no change the the relative growth rates of the 4 species used vs the controls with roots.
So the roots really played little role when the water column is nutrient rich.
That's what is known and what is the research.....at least for those 4 species......
A better focus should be on the consistency of supply so applying the assumption that the plants can get the nutrients from BOTH source would be a wiser approach.
That covers both assumptions.
Unlike this "either or" business
Another question is do you honestly want larger sword plants?
Crypts? Generally not either.
I know these plants do well in both situations, but other plants need water column fertilization as it targets all plants well for most any scaping design one might have.
Still, adding ADA AS, or a sediment with good river clay/swamp soil and some sand can certainly add to the water column and adding ferts to the water column reduces the amount of nutrients required from the sediments as well, thus you get more out both than you do from "either or".
Less critical water column dosing and longer lasting sediment nutrient source.
This makes the assumption that some plants do prefer sediment uptake.
We really do not know this, but it's still a safe assumption given the trade offs.