I assume that the $1000 and $100 examples are hypothetical?
If not, then there is only one answer: there is no "vs." $1100 gets you
both. Go for it.
Practicality forced me into headphones. I never liked them. Now I love them, and hope to move up to $1,000-plus spend on them. I do suspect that the result
within the limitations of headphones might well rival
$10,000 on a speaker setup.
I do not find my headphones fatiguing in the audio sense, but it does get a bit steamy in there on a hot night! Apart from this, they are entirely comfortable, and I could forget I'm using them.
Headphones put the music inside your head --- and give the feeling of being inside the music. It is a different experience. Headphones cannot give you the music spread out in front of you, although our imaginations do help a lot with that.
If you want to go for headphones, do the headphone-specific research. Open or closed? Light-weight, or can you stand half a kilo on your head.
Do remember: with headphones, you can
never share your music.
Unless a person is aiming for some really high-end 'phones setup, this just not have to be an either/or question anyway: have both
my setup:
PC --> ODAC --> Pre-amp (allows other sources with easy switching) --> ifi iCAN --> Audio Technica AT-ADH900 open-back, light-weight 'phones.