The Boeing 737MAX cannot use the Pratt & Whitney Geared Turbofan or GTF engine design due to inadequate wing ground clearance. The Airbus 320NEO has a higher wing ground clearance and thus is able to use the GTF engine design. This may give the 320NEO an advantage on the engine front.
A possible solution for the 737MAX may be additional side exhausts for the LEAP engine to get more power output from the fan of the engine. It can even be optimized by using Harrier type nozzles to adjust to thrust angle needs. The disadvantages are it will be more complicated, more weight and heavier drag.