Looking at the specs for both the GT2 belt and the Synchromesh I'm very hesitant to recommend a Synchromesh over a belt.
The first thing that sticks out is that there are both error and cumulative error specifications for the Synchromesh. For a device like a 3D printer, I don't like the idea that of my axes can accumulate up to ±0.16 in. of error over 100 pitches (the pitch is between 0.12 in. and 0.25 in. so that is 12 to 25 in.).
Contrast this to a belt where the only way you have a cumulative error is if you skip a tooth and I think the winner is the GT2.
Looking at the non-cumulative pitch error both products are comparable but again the belt wins. For the Synchromesh we have an accuracy of ±0.002 in. versus ±0.0003(1) in. for a 2 mm GT2 belt and ±0.0012(1) in. for a 3 mm GT2 belt.
Note: I can't be certain about exact values for error since there are no numbers for the GT2 - only a stupid chart. I also have a hard time believing that error is not a function of total length for both the Synchromesh and the GT2 belt but I'm not the manufacturer. However, since both products are made by the same company I wouldn't be as concerned about them trying to oversell one product over the other.
In conclusion, I don't see of any reason to choose a Synchromesh over a belt if your physical layout is compatible with both. As pointed out in the marketing material for the Synchromesh, it can be routed along 3 axes whereas a belt works best along a single axis. The Synchromesh seems to be a product designed for a very specific application...