Yes the resolution is the same. You simply have to feed the 1.75mm faster, but with less force to get the same flow rate as 3mm. It is roughly the same as adding more gearing but without backlash.
Smaller nozzle diameters get better resolution but the force required to extrude goes up as a fourth power law, so it gets impractical below about 0.2mm. Also the build speed goes down as a square law so it takes an impractical amount of time to make something big with high resolution.