Engine replaced with 20,000 used, we have checked fuel pressure, performed normal tune up procedures, cleaned fuel rail & injectors, reflashed the computer, replaced filters. The engine starts quickly and runs very smoothly. It always hesitates when pressing the accelerator. The only other problem is that it seems to be very underpowered, like there is no power curve. Interestingly, the old engine had slight hesitation when pressing the accelerator. I would appreciate any suggestions.

Check your intake that it is sucking in air correctly and that your throttle body isn't stuck.. Try a rad flush.. maybe also try a thinner oil... [5w30]

I had the exsact same issue two weeks ago. I replaced the Mass airflow sensor and everything is peachy now! watch to see when it cuts out. If the power drops off at 3000 RPM try then you may have the mass air flow issue.

Thanks to all who responded. We replaced the Mass Air Flow Sensor and voila, the problem is solved. For some reason the MAFS does not invoke codes on the computer.