Digital potentiometer step size
Replacing a 5 k&Omega; pot with a 20 k&Omega; pot and then using just 1/4 of the range isn't the same.  The output of a potentiometer is ratiometric, meaning it is relative to the voltage at both ends.  It is a linear blending of the two voltages, with the wiper position setting the blending factors from 0 and 1 at one end to 1 and 0 at the other.

The difference between the 5 k&Omega; and 20 k&Omega; pots is the output impedance.  This is highest in the middle and goes towards 0 at each end.  For the 5 k&Omega; pot, in the middle setting there are effectively two 2.5 k&Omega; resistor in parallel impedance-wise.  That makes its output impedance half that, or 1.25 k&Omega;.  All this scales up by a factor of 4 for the other pot.  In the middle, it has two 10 k&Omega; resistor in parallel, making the output impedance 5 k&Omega; worst case.

Whether the higher output impedance matters depends on the circuit and is impossible to say with the information you have given us.  If the circuit that receives the pot output signal loads it too much, then the result will be non-linear.  Whether that matters is again a function of the circuit you have told us nothing about.

However, you are right about the resolution.  The 10 bit pot has 1024 unique settings, which will make the adjustment smoother than one with lower resolution.  Note that this is only a issue when the pot setting is being changed.  A 10 bit pot at a fixed position produces the same output as a 8 bit pot in the same position, but the 8 bit pot can't be set as precisely as the 10 bit pot.

Explain what the application is an show the circuit around the pot, especially where the output signal is going.