Well yes. But I heard that the battery is smaller and I can tell
Smaller battery to what, the 6?
Yes, it has less capacity but the difference is negligible. Its barely a 5% difference in capacity and the more power efficient parts of the chips in the 6s offset that difference, and they should be about the same.
I can tell you from my experience with my 6, running on iOS 8 and my 6s, running on iOS 9 that the 6s with iOS 9 and battery saver mode has a better battery life.
I am not sure what your battery issues are, based on your description it is not normal battery behaviour, but I wouldn't be so quick to label them as a result of the smaller battery in the 6s. Its a negligible difference at the end of the day. Your issues seem to be due to a faulty battery. An iPhone 6s should give you a day's worth of battery life no problem.
If you're not using 3D touch you're missing out on one of the best features in any smart phone to date. It may not be everyone's cup of tea, and you can turn it off, but man if you get used to it, its beautiful. Improves workflow a lot.
Also, the 6s is a quantifiably better product than the 6 (which should be a given since its the next generation iPhone) - its got a stronger body, stronger glass, faster touch ID, 3D touch (which doesn't seem to be a selling feature for you but oh well, you're missing out), excellent camera especially for videos, a much more powerful chip in the A9 and the big one for multitasking is 2GB of Ram - among other improvements (some of which future proof the device, such as the new LTE and Wifi chips)
All in all its a great device and if you feel like it wasn't worth the upgrade for your needs, then fine you have the right to feel that way (and you know your needs better than anyone else), but don't expect to create a thread complaining about something and not receive feedback that suggests otherwise.