Thickness
Besides the thickness difference (1cm = 3/8″ 2cm = 3/4″ and 3cm = 1-1/4″)
Preparation
With most 3cm slabs you can install them right on top of your cabinets. Whereas, the 2cm requires a plywood subtop. Which most contractors will install prior to the countertop installation.
Edge
If you’ve ever noticed while antique shopping, all of the marble tops are 2cm. Its because its the original thickness. Back in the day, having natural stone in your home was a major luxury. The thinner thickness gives you a lot more options for ornate edges, in which they laminate another strip underneath, making it appear thicker. The 3cm thickness only became popular in the last 20 years or so.
Overhang
Overhangs beyond cabinets may extend 12” without support with 2cm granite combined with ¾” substrate. Unsupported overhangs beyond 10” are not recommended with unsupported 3cm granite.
Backsplash
With 2cm you can apply a fullheight backsplash with no extra prep (besides rodding for stability during transportation). The look is much sleeker and your cabinets will thank you for them being lighter weight. 3cm splashes create a much bulkier presentation and on standard cabinets may cause less area for counter space and placement of faucet holes above sinks. You can however have your fabricator can guage down the thickness to 2cm for a sleeker look.