The Apple TV HD is much, much worse in every way. It's a really old repackaged model from like 2015 that Apple hasn't bothered updating. Definitely get any of the Apple TV 4K models, even the first-gen 4K is better.
The HD doesn't get:
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4K support (1080p max resolution)
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HDR/Dolby Vision
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Dolby Atmos
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Worse connection speeds (100 Mbit max on the HD, 1000 Mbit on 4K, slower wifi and bluetooth as well on the HD)
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No Homepod support
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No smart home stuff
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The CPU is much slower with an A8 (HD) vs the A15 (4K). Literally seven CPU generations slower.
I would not even remotely consider the Apple TV HD unless it was like $20. It's outdated in pretty much every way possible. The Apple TV 4K is modern hardware, and will remain modern for at least 5+ years from now. My parents inherited my first-gen Apple TV 4K and that box is still fairly modern by todays standards, and is better than the Apple TV HD.