I have been using the gravity app, and have not noticed a significant battery usage. A little, but I like it so much that I honestly wouldn't care if it had more drain on the battery. The Pixel charges so fast it makes it a non issue for me.
It's a great phone, you wouldn't regret upgrading. I get a day out of mine, but the best thing is, it charges in about an hour. So you aren't tied to a cord half the day.
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I bought mine through amazon a few weeks ago, 32gb, on sale, for $375. It was new and I have had no issues with it, can't find any flaws. I bought the black one, which is what I would have ordered from Motorola anyway.