I have no idea really. We are kind of on the bleeding edge of consumer health tech.
I had some workouts get duplicated just through application syncing. So I had to redo the sync setup between applications. I've also had issues where S Health and another app both log the same thing. In the event something like that happens I just go in delete duplicates.
You can do some tests to see what will happen in the dual use setup. You can delete them from the history.
My guess will be you want to just use the the phone's logging while using the chest strap. If you can log both simultaneous it may make for an interesting comparison between the two devices. Some people have different results but I've found the watch to be accurate. It samples in a resting state about every hour and appears to sample every few seconds while logging an activity.
The advantage of the watch is being able to leave your phone behind and track or just have it track simple daily activity levels. I never want to run with my phone again since it's a phablet.