Macro algae= you will need higher nutrients, mostly NO3, but they will take up more and are a bit more trouble to tend than ATS.
ATS: able to respond well to lower ppms of NO3 etc, but...........so can a NO3 bead reactor, so can a DBS etc.
ATS will remove PO4, but a well run macro tank can also, if fact, you might need to add a pulse here or there for the macros not to become too PO4 limited so they can maintain the NO3 uptake rate.
Both Refuge's and ATS's need some biomass export for removal, this also maintains the biomass to keep the removal rates of N and P relatively constant. You do not want feast or famine uptake rates, this leads to algae feast or famine in your main tanks.
Stable biomass= stable uptake rates.
ATS's are good for some critters as a source of food, while macros are preferred by others, this is a consideration also.
Macros look much prettier and can be sold, ATS? Not so much.
ATS's are better as utilitarian filters, and sunlight, windows etc can be used very well. ATS's also can provide good evapo transporation to cool the water down if you do the trickle over the vertical sheet method etc.
Something that might avoid a chiller for some aquariums.
Well engineered and thought out, the ATS offers a fair amount.
It's a more robust system, but a dense refuge looks good, has much nicer diversity and can do essentially all that you might need for a reef display. Yes, the ppm's/ppb's are tad higher to keep the macros going, but this translates into nicer coral and zooxanthellae. They will grow and use the ferts at low levels also. Depending on your feeding routine, the PO4 is the main control factor.
Some folks just feed more to prevent strong limitation of the macros by PO4, this in turn feeds the coral even better, and then the waste is removed rather quickly by the macros and the DBS in the refuge along with the fast growing macros takes care of the NO3.
Both systems can work well.
I think coral growth is likely better from what I've seen with the refuges that are managed to keep the relative same/similar biomass(eg, they prune once every 1 to 2 months etc).
Tang's gotta eat.