As indicated in the comment above, "magic numbers" (i.e., atom counts with much higher stability) have been known in atomic clusters of many types for a long time.
Each magic number has a specific geometry. Some are non-spherical, so it's hard to make generalizations about surface area or lattice structure.
A very famous non-gold example is buckminsterfullerene ($\ce{C60}$). Multiple groups had seen the signature of 720 Daltons in mass spectra of soot for years before the official discovery. There are other magic numbers for $\ce{C_n}$ clusters.
In nanoparticles and nanoclusters, this is an active area of research, but the main difference is stability. The so-called magic-numbers are simply more stable. (Case in point, the thiol-termated gold nanoparticles were created by heating up the samples until only the most stable ones survived.)
While I'm not an expert, I suspect the increased stability likely means less reactivity, lower catalytic activity (i.e., the species is more stable, less reactive so less likely to activate).
I'll give a comparison with Hückel's 4n+2 $\pi$ electron rule. We know that benzene is aromatic and has increased stability relative to the 5-membered and 7-membered conjugated hydrocarbon rings. It's less reactive and thus requires specific reaction chemistry.