There is no doubt that the GPS services drain the battery much faster than office / alert use. I think the heart rate monitor might be a battery hog as well, so it might depend on how often you sample the heart rate.
The Gear S is a great watch, but it in no way replaces my Garmin. Garmin is also starting to add some alert features to there newer watches, but they are not up to the level of the Gear S. ... Plus they don't have a cell feature. I often take both watches when I'm on long bike rides for 2 different purposes.
I do use SHealth on the tread mill since I don't have a foot pod for the Garmin anyway, I don't notice significant battery drain there.
In the next couple of iterations of both sports watches, and smart watches I think the line will become quite fuzzy, but at this point if you want to do serious sports tracking I recommend a sports specific watch (Garmin, Polar, Mio, Timex, etc).