I would guess it should be around the same, maybe better. The 835 is probably more efficient, and since the difference in battery size between the original and new Pixel is only 70mAh (almost nothing really), I doubt it would drop any. If that holds true, I'll be fine even if it's the same as the original Pixel.
That is my biggest question as well. I am very happy with my Pixel battery life. Roughly 4 hour 15 minutes SOT and standby drain is perfection. If Pixel 2 can improve on that I will be happy. sD835 should be a lot more efficient, however I am more concerned with screen and other component drain.
It's kind of too early to ask this question. No one here can truly answer this since none of us have the phone yet. I say just wait for official reviews to come out.
Of course you know the first day someone posts they have received the phone and comments on its battery life after 2 hours of use, there will be the normal histrionics, hyperbole and hand wringing. Always fun
I'm hoping that the well reported changes in Oreo 8.0 will improve battery life. It is supposed to limit background processes that have drained the battery in previous operating systems.
As dsignori mentioned it will be important to wait for things to settle down and see what the real results are after things stabilize and some real results begin to appear.
If battery life matches or slightly exceeds the first Pixel, I'll be fine with it. My original Pixel has always lasted the day even on a heavy use day. No battery complaints here with the first Pixel. I hope to be able to say that with the Pixel 2. I'll find out when my Pixel 2 gets here later this month.