The short version
The Ultrahuman Ring Pro is the subscription-free flagship — one-time $479, ~15-day battery, on-ring processing. The Oura Ring 5 has the more mature app, from a ring line with more research on earlier models (the Ring 5’s accuracy has not yet been independently validated), at $399 plus a mandatory membership.
When is the Ultrahuman Ring Pro the right pick?
You refuse a recurring fee, you want the longest battery in the category, and you’re fine being an early adopter of a redesigned ring.
When is the Oura Ring 5 the right pick?
Accuracy and app depth are the priority, you want upgraded sensors and the most polished experience, and the membership is acceptable.
Also worth comparing
For the previous, cheaper Oura, see Oura Ring 5 vs Oura Ring 4; for other subscription-free rings, the Samsung Galaxy Ring and RingConn Gen 2. Full field: best HRV trackers.