Not sure which would be faster, but it's a better long term solution IMO.
Some Corals need some nutrients in the tank, just at low levels. When chemically filtering them out, you are also keeping the nutrients from the bacteria in the Live Rocks, the corals as well as the algae. And if the chemical export mechanism is saturated or becomes less effective, the other parts of the biological system may be less capable of handling the excess. If it is stripping too much, then your corals may suffer and youyr bacteria colonies may not be quite as resilient.
IOW, you have to balance "too much" and "too little" with the chemical filtration, which is further complicated by the fact it's not constant with fresh media vs. old.
Even very efficient macro fuges or algae scrubbers allow some nutrients to exist in the water column, and can react to larger or fewer nutrients more or less automatically by their growth rate. And when you trim your algae, you are completely exporting those excess nutrients. I find the balance to be easier. And my chaeto has all kinds of little critters running around in it, so more "stuff" to be in the water column for the corals and even fish to eat. I'm experimenting with a SantaMonica DROP .6 algae scrubber right now (which would address the excess light issue), but it's too soon for me to say whether that's more or less effective than chaeto.
Certainly things can go wrong with either system, I guess I'm just a bigger fan of a more natural approach. And if you're skimming already to remove the dissolved organics, then the fuge would be about all the additional filtering you really need.