What is the range difference between LEAP and PW1000 powered A320 and A321 NEOs?
According to Airbus
Airbus quote a single range figure of 6300km for the A320neo
This is 100km more than Airbus claim for the A320ceo with sharklets but the difference is probably due to increased fuel capacity in the A320neo and possibly to revised wingtip arrangements.
The difference in range between older A320 (~5700km?) and A320 with sharklets (~6200km) appears to be 500km. This implies the wing sharklets are more important than larger fuel capacity and both these features are more important than engine differences alone.
Superficially at least, the choice of engine does not affect the range claimed by Airbus.

This raises the question, what benefits are provided by the new engine options alone?
The only relevant claim by Airbus appears to be

The A320neo also offers significant environmental performance with nearly 50% reduction in noise footprint compared to previous generation aircraft.

I guess airlines choose between NEO engine options mostly based on commercial factors and maybe on fleet characteristics, maintenance arrangements, etc. Factors other than range.

According to others
Forbes has a comparison beween these two engines which suggests the geared-turbofan arrangement of the PW1000 offers large advantages in both fuel efficiency and noise.