You have a dirty mas airflow sensor. Remove the air filter, remove the MAF assembly & clean the element(s) with alcohol & dry....you won't believe the difference! Mine ran crappy & stumbled & died many times, thinking it was bad gas...cleaned the sensor...runs like new!

 

I have an 04 f150 5.4 ,but it only sputters when I floor it. Could this be the same problem? Does the 04 have a recall on the pressure regulator too?