It's a vexed and personal topic.
Headphones are cool and a good pair is a wonderful tool but a) they aren't "stereo" (now, binaural recording is a different matter) & b) they create GREAT mixes for headphones.
Regarding headphones versus stereo here's a good guide/intro...


I started recording monitoring through a stereo system. I moved, eventually, to "monitors" and they difference between the previous & the new was amazing and allowed me to get a much better picture of my stereo recording though, with only 41/2" woofers I was ALWAYS guessing bottom end...and headphones don't really help with that - even a nice pair of open back Sennheizers aren't particularly "true". I now have new "monitors" with a 7" woofer and I'm taking time to get to know them before doing any critical "work" but I do now I can actually hear rather than psycho acoustically create in my head, the bottom end. I don't use a sub because I'm still unhappy with the crossover part of that world.

Headphones play an important role though...detail listening...scanning for "noise" etc

Cheers
rayc
"What's so funny about peace, love & understanding?" - N.Lowe