I am fortunate to have both (or spent a stupid amount!). I have a 5.1 surround sound system with my gaming PC, but also a number of respectable headphones with dedicated AMP's and DAC's.
Most of my game play is not overly competitive so really love the power and feel the 5.1 system can provide. hearing sounds from the rear and each side independently along with a sub can kick out a more visceral sound and find the fun factor much higher.
However when I need to tone it down to stop having booms annoying other's or went to go slightly more immersive at the expense of a beefy sound (does that even make sense!) I will go to headphones and similarly there have an absolute blast. Once again, not overly competitive, so will use my more fun sounding (AKG 712's, HD800s, HD6xx etc) headphones rather then say my AKG 702's which can pick out every tiny detail.
So yeah, TL:DR, for me speakers, and more so surround sound is my number one pick, however headphones are extremely great but even then I prefer fun sounding ones which give up say the ability to pick up every detail for a more fun factor.