If water, air of whatever fluid had a different viscosity, but the same density, would things fall/sink differently?
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$\begingroup$ [Related Quora Would-a-hydrophobic-coating-make-a-heavy-object-sink-through-water-faster] (quora.com/Science/…) $\endgroup$ – user28737 Jun 4 '14 at 6:07
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Yes they would fall differently.
For example, according to Stokes' Law the drag force is proportional to dynamic viscosity and the terminal velocity of a falling sphere is:
$$\frac{2(\rho_s -\rho_f)}{9\mu}gR^2$$
where $\rho_s$ and $\rho_f$ are the densities of the sphere, $\mu$ is the dynamic viscosity, $g$ is the acceleration due to gravity, and $R$ is the radius of the sphere.
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The dynamics in case of relative motion will be different: e.g., the acceleration and terminal velocity when falling/sinking. But the equilibrium will be unaffected (e.g., floating and waterline). This is because viscosity is at the origin of a frictional force.
