I went from the SE to the S8, and the SE had the same sensor as the S4.
I believe the sensor has been updated between S4 (or SE) and S5 but in my experience it's no magic bullet. With both watches I found I had better success with a higher strap and also with starting the heart monitoring before the exercise.
I'm speculating that the watch has trouble identifying the heart rate when the watch is moving (while exercising) and while the heart rate is changing (also while exercising), so at the start of the exercise it's a significant amount of both of those things that have to be overcome. Once it's got a baseline heart rate I'm sure it's easier for it to filter out any "noise" from the watch movement. I might be completely wrong of course. Regardless, whether S4 or newer, I would be starting the heart monitor before exercise.
One exercise I do in the winter is running up and down the stairs of my apartment building, which feels to be more "bouncy" than running on a treadmill or outside. For the first 10 flights of stairs I hold the watch firmly against my wrist and that seems to lock in the heart rate pretty quickly, and then for the balance it's good. I never need to do this while running outside, but I have found that on occasion running outside I get gaps too.
Re-reading that it reads like a bit of black magic. Again, I might be totally wrong but anecdotally:
* Keep the strap quite tight. I use the Nike straps and move up by one hole.
* Yes there is a minor improvement in the sensor, but it's certainly no magic bullet.
* Regardless, start the heart monitor just before you start to exercise (perhaps a minute).
* When I'm running up and down stairs I hold the watch to my wrist for the first portion.
