Are you basing this on observed battery life, i.e. the time from when you unplug the charger at 100% to the time the phone switches off, or are you basing it on Battery Saver's prediction? If the latter, when was the last time you recalibrated your battery - ran it down until the phone shut off, then charged it to 100%? Lithium ion batteries need to be calibrated every few months or the percentages reported, and therefore the prediction algorithms, gradually drift away from reality. Don't do it too frequently, as it will cause battery deterioration, but once in a while is necessary.
All other things being equal, 8.1/Cyan is supposed to give better battery life than 8.1/Black, although I'm not expecting a miracle. I don't have a good basis for comparison to 8.0, although some suggest they should be in the same ballpark when set up similarly, whereas others say 8.1 is a bit worse. If it's a lot worse, something's wrong, prompting solutions such as soft resets, battery recalibrations, opening each of your apps and making sure it's properly set up, etc. Also, check in Battery Saver for what's using the most power - might be an app that needs to be uninstalled and reinstalled.
On 8.1.1 DP/Black, I was getting real 100% to 0% times of 18 to 36 hours on a charge, based on Battery Saver's predictions when I put the phone on the charger after 15 or 16 hours (NOT when I took it off the charger). I've only had Cyan for 2 days, so not sure how it's going to compare yet. So far, might be a little better, probably not worse.