I've done it both ways. Keeping track of paper and pen and taking notes is more complicated than just having something strapped to your wrist that does it all automatically with an occasional swipe or tap. Both ways are pretty simple so I don't want to exaggerate, but having the thing automatically do the thing is definitely simpler.
The random quirks of software are complicated... that's the world we live in though. New stuff is developed to replace the old stuff before we've even worked out the kinks in the old stuff.
I don't use an apple or high fashion watch for this, and while GPS and payments work, I don't have LTE for messaging like many do. A lot of watches are just a step up from a fitbit. Fitbit with maps I guess. Hmm, maybe I should have just gotten a fitbit. :)
If I were still a runner, I would buy an Apple Watch in a heartbeat especially now that it has cellular. Heck I would buy it if I still went to the gym (as opposed to having my home gym) just so I could leave my phone in the car.
Apple watch just doesn't cut it. I own both (AW2 and Garmin 735xt) and I gave up trying to use the AW for any of the sports that I do. (Running, swimming, biking, gym, Triathlon)
There is no way to do all that properly with an Apple Watch as of today. Not to mention the pain that is to wait for the screen to turn on to see if you are running at the proper pace/HR vs a Garmin watch.