Neither monitors nor headphones are sufficient
If you ask me (which I now you didn't do directly), both are necessary to ensure a good product, regardless of whether pro's use headphones or not. Remember that some people will listen to your recordings through a stereo system in a car, home, etc. and some will listen through headphones. To lsiten through good monitors and sya that it's good for headphones as well is to miss a step.
Headphones are the BEST way to analyze stereo definition; they completely isolate the Left/right channels to one ear apiece. If something sounds too centered or symmetrical with headphones, then they're going to sound even more mono through speakers (usually, depending on the system). For example, if you record guitar to a mon track, it might not sound THAT bad through speakers, but when heard through headphones (which CLEARLY show how mono it is), then it sounds like shiste.
For those who think that "monitors are better than headphones, so if you have good monitors, don't use headphones," I'm afraid you are missing out on an analytical tool. Good monitors and good headphones in combination provide better access to ANY recording.
HOWEVER, make SURE that your headphones do not have some sort of gimmick like "Uber-bass enhancement." You want a FLAT freq response.
A doctor doesn't use one tool to do surgery. Why would using only monitors be better than using both? Well, it isn't.