I have since got both hands free devices to work correctly, but I am not entirely sure how ...
I did two things, so can't be sure which one fixed it. First I unpaired the devices from the iPhone and then shut down the phone and restarted it. Second, I paired the Jabra device and then played a video on the iPhone. The sound came through the Jabra. I stopped the video and answered a call - and the voice worked both ways through the Jabra. With the Jabra powered off, I paired the iPhone with my car audio system - and it worked. now I can pair the iPhone with either device and it works, which is good, because my car system is convenient but has a poor microphone, whereas the Jabra requires manual steps to turn it on etc., but the person on the other end of a call can hear me much clearer.
So, I am guessing that the upgrade to iOS 5 confused the hands free status and that was cleared either by the restart with no hands free device paired OR by pushing another audio stream to the Jabra (which can also handle stereo audio into a car radio via FM modulation). I won't be able to verify that until/unless the original problem appears again. If anyone else can try one approach or the other and then retest, I would be very interested in the results.