Looks like I'm late in the debate!
I say they both have their place! One is for one type of aquarium, while the other is for a different type of aquarium. A fish only aquarium can only benefit from protein skimming for nutrient control. Heavily stocked reef tanks will also benefit by the use of a protein skimmer. However, a mid to lightly stocked with fish reef tank iis a perfect candidate for only using an algae scrubber. Algae scrubbers can be used on heavily stocked fish only tanks or heavily stocked reef tanks successfully, but take up a lot of space because they have to be doubled or tripled.
Algae scrubbers add dissolved oxygen to the system. They stabilize pH at night, they maintain constant alkalinity. It's a great way to cool your water with a fan. They increase magnesium in the water column (I'll try to post this research) They remove nitrate and phosphate while leaving in coral foods such as bacteria, sponges, detritus, forams, pods, other detrivores, free floating cyano, phytoplankton and all manner of zooplankton. (some listed). Algae scrubbers can also remove heavy metals such as copper and iron. By using an algae scrubber, you remove the dissolved organic nutrients such as inorganic and organic nitrate and phosphate while leaving in particulate organic matter (POM) that corals eat and protein skimmers remove.