apple-watchhealth-kit
I have found the corresponding Activity app on the iPhone, which shows exercise history, but is there a way you can see the history of each heart rate measurement in bpm? Maybe through a HealthKit application?
EDIT: Thanks to bmike's suggestion, I found the export function of the Health app on the iPhone. The button in the upper right lets you send the raw data as an XML file.
If the watches are different, and the phones are different, then the only thing that appears to remain the same is you.
You don't mention, but have you ruled out the possibility of there being anything about you? For instance, I remember reading that tattoos could prevent the heart monitor obtaining a clear reading, and there was some talk about people with very black skin also having difficulties. Example article here http://www.bbc.co.uk/news/technology-32537030
The other possibility is whether there is something with the tightness with which you wear it?
I went for a 2:30:00 run yesterday with my iPhone (6s) in my bag and my watch running strava. VO2max was recorded once per hour in three hours (10-11/11-12/12-13). I’ve tried to get VO2max off of shorter runs (5k-10k) on the same route without my phone but no data. I will now have to test longer runs with just watch and shorter ones with phone to get a definitive answer. Hope this is helpful. 
Best Answer
Apple allows you to inspect all data using the Health app itself. In addition to the graphs it prepares, you can tap the graph and then Show All Data
As you know, there's no export function on iOS itself, but there's no reason any third party app can't request access to that data (which you also can see and approve from the Share Data tab of that app.
I would check out apps like: