While I can't tell you which phone is best for you. I just ditched my Note 3 and moved to Moto X 2nd gen. Here are my response to the 4 concerns you listed:
1. Battery: Yes, Moto X does not have the best battery life but still enough to last me for one day use. With chargers in the office and in the car and portable battery charger, I don't see this as a big issue for me.
2. QHD: not going to miss what I don't have and Moto X's screen does just fine for me.
3. Camera: Moto X is not as good but for taking random shots and post to social media, it does just alright. Not a huge con for me.
4. S-Pen: Never really used it with Note 3, doubt I will be using it more with Note 4.
Here are my list of why I picked Moto X instead of Note 4:
1. Want a device with smaller footprint, while I never had a huge issue of carrying note 3 and love the large screen size but at this point, I want to drop down to a smaller device.
2. Moto Assist, Voice, Display, Action are awesome.
3. Close to pure android experience is always a plus and faster update to Android L
4. Moto Maker and the leather back... need I say more?
5. Getting a little tired of Samsung's TW and want to try something different.
6. It's cheap enough for me to just buy it outright and don't have to worry about contract.
Since you will be using this phone, you will have to decide which one is better for you, I was very much on the fence between note 4 and Moto X and finally decided I will give Moto X a try.. so far I am loving it.