The fundamental difference between speakers and headphones is the way in which the soundfield is presented. With speakers, if you turn your head to one side, look behind you, etc., then the soundfield will change because the position of your ears has changed. With headphones, the soundfield is consistent, even if you turn your head etc. Heck, with wireless headphones (or a long enough cord) you can go to the kitchen ( or the bathroom) but the soundfield will still place you in the thick of things.
One secondary consideration is that, for the same amount of money, you can get much better sound quality from a pair of headphones than you can from speakers, because for the latter you will need at least 5 speakers plus a subwoofer. For example, $500 will get you a much better quality headphone than speakers.
Headphones will certainly give you a 3 dimensional immersive soundfield though so you do not need speakers "for the directional stuff" because you will get that in the headphones. So for the question you asked, yes, headphones will do the job you want them to do when it comes to playing FPS.