Can headphones ever be as good as high end stereo?

I am absolutely satisfied with the sounds of my current setup but I feel like I'm unable to listen at the volumes I prefer on a regular basis due to the ole spouse. I've been considering switching over to headphones. By selling my current speakers and amps I could easily finance stax 009 phones and a suitable amp, which seem to be regarded as the pinnacle of headphones.

My question is, what would I be losing or gaining in the switch? Right now my setup emits a beautiful wall of sound and I would hate to give that up. Understand that I have never owned a pair of headphones worth more than 80 bucks so I have no idea what good ones sounds like. Almost all source material would come from a pyon ultima table. Thanks