I didn't get the 6s, so I'm not going to vote in the poll, but after observing my coworker with his 6s, I feel like I would use 3D Touch frequently for some things and not at all for others. For example, quickly starting a text from the home screen, getting insta-directions home on Maps, or taking a new picture with Instagram. Outside of those 3, I don't think I'd use any of the other shortcuts from the home screen, but of course I could be wrong since I don't personally own one.
The only "useless" 3D touch gimmick to me is the "press hard on the home screen to see your live picture move" one. That doesn't make sense to me. Partly because Touch ID is insanely fast if you unlock with the home button so you won't even see the picture, and partly because if you DO use the lock/wake button to wake up the phone, who wants to have to press hard on the screen to see it move? In my opinion, it would be much better if the picture moved each time you woke up the screen. 3D Touching the screen would instead change the background to a different live picture, or maybe start a little slideshow.
I just think the live pictures' potential is a little wasted because I know I would seldom press on the lock screen, and would much rather see it move automatically each time it's woken up like on the Apple Watch.