I get very good results with a Sony X1000. Software stabilisation and good enough at HD (not 4K) 50/60fps. The battery runs for about 2hrs which is about the same as all action cams.
The Sony X3000 is no good because the optical stabilisation can't deal with the vibration spectrum; it is probably fine on a helmet.
The DJI Osmo Pocket is completely useless because the gimbal system also can't deal with the vibration. This is in the proper bike mount, too. It would be fine helmet mounted. It does produce the most awesome ski videos when handheld
If I didn't already have the X1000 I would buy a used Go-Pro Session; it is a nice compact package, has loads of mounting kit options, and does a good HD / 60fps video. You do want 50/60fps for biking; 25/30fps is OK for documenting bad drivers and such but the result is not really watchable. New action cams can do 4K at 60fps but the required data rate (at least 50mbps and ideally 100mbps) fills up CD cards very fast.
I hope these are useful data points for someone.