The short version
Oura wins on analytics depth and app maturity; RingConn wins on battery, subscription model and total cost. Most users land on Oura for the polish; the minority who land on RingConn are the right minority for the subscription-free model.
When Oura Ring 4 is the right pick
If app maturity, the deepest consumer sleep model and Readiness scoring are the deciding criteria, Oura is the right shape. The $5.99/month membership is the cost of admission to a decade of iteration.
When RingConn Gen 2 is the right pick
If subscription-free is a hard requirement, you want the longest battery in the smart-ring category and the lowest 3-year total cost of ownership matters, RingConn is the right shape. The trade is a slightly less mature app and shallower sleep analytics.