It's Strava's fault. I did a 30 mile ride over the weekend. Halfway through I stopped to make sure the info showing on the watch was also syncing to Strava. Not sure what happened, but both the Watch and iPhone app immediately zeroed out and I lost half my ride.
For the second half of my ride, I used the Watch's exercise app and Strava independently only on my iPhone (removed it from the Watch to avoid any problems). Both measured the ride effectively, so I'm pretty sure you don't have to choose between the two.
One other thing, and this may just be a bug, but it seems like the official Watch exercise app is able to "take over" when you are in the middle of working out, so that when you tilt your Watch it shows not the watch face, but your exercise progress. As far as I can tell, third party apps can't do this (when I tilt to see my Strava progress, it instead shows the watch app). I know there is a setting to always show the last used app, but I would rather keep the default behavior.
This is probably a Strava Watch app deal-breaker for me, as I'd rather not take both my hands off the bike to check my Strava progress. On the other hand, I really enjoyed using the Watch exercise app; having my current speed available motivated me to push myself and break some Strava records (running on my phone).