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Doze should mean the battery life is OK, quite a lot of people seem to reckon it's alright.
The lag thing seems to develop after a few days use, the phone then needs restarting to get rid of it. The consensus is it's a software issue which Google can fix, but there is apparently a consistent camera lag if you take multiple HDR shots in a row. That wouldn't bother me personally, but YMMV. I don't know if the 6P also has that issue.
I had a good play with one today and couldn't get any lag at all, although I didn't do multiple pictures.
There's some good info here:
https://www.reddit.com/r/nexus5x/comments/3zgfd1/are_there_actual_5x_users_with_no_problems_with/
You mean the lag? If so, yes, that's what putting me off too. Well, that and not having the cash. Hoping software updates will fix it as a 5X would be perfect for me. Not keen on rooting a brand new Nexus.
The Reddit 5x forum is worth a look if you've not already.