When to use 1.75 mm vs 3 mm filament?
There's no appreciable difference. Just use the filament that fits your particular printer.
If you don't yet have a printer, then I'd get one that uses 1.75 mm filament:
1.75 mm is increasingly becoming the "standard", thus being easier to get. Some filaments are not available as 3 mm.
1.75 mm filament allows for finer control, because feeding in 1 mm of filament corresponds to less plastic extruded.
1.75 mm filament requires less force to extrude. Compressing 1.75 mm down to 0.3 mm takes less force than doing the same to 3 mm filament.
However, the advantages are fairly minor. I don't see any reason to replace a functioning 3 mm extruder with a 1.75 mm one (yet).
You mention some very good points! Do you think this mean printers with 1.75 mm extruders struggle less with - for instance - stringing?