For me, it's not either/or but both/and.
I enjoy listening to my Spendor speakers, and I also enjoy music through my Sennheiser HD800 headphones.
The HD800s were game-changers for me. Like you, I had mainly owned modest headphones before, some basic Grados, and a more expensive pair of AKG 702 (the 65th Anniversary edition). The AKGs made me realize that headphones can be better than I had thought. And now that I have the HD800s, I thoroughly enjoy listening through headphones.
The HD800s have an actual sense of soundstage, unlike headphones that put everything between your ears. They are comfortable, at least on my head. And they sound superb driven by OTL tubes amps, including a modest little Bottlehead Crack and a Woo WA2.
I mainly listen to classical and jazz, and I do like to turn it up when the music demands. The HD800s remain clean at high volumes. (Not ear-damaging levels, of course.) And I don't find them to be bright, at least not when driven by the tube amps I use.
One caveat -- I don't do vinyl. So, I can't say whether record surface noise or turntable mechanical noise would be exacerbated through headphones.
I haven't tried Stax electrostatics--and am in no rush to do so, given how much I like the HD800s.
I might sound like a salesman for Sennheiser but I have no affiliation -- just an audiophile and music lover happy with a purchase.