After optimizing my FP2 with FP Open, Xposed, microG and UnifiedNLP (GSM Local Backend and Wi-Fi Local Backend) I have now a perfectly stable phone with excellent battery performance. I tested battery consumption with three setups: Wi-Fi allowed to sleep, Wi-Fi always on, and 4G data instead of Wi-Fi (Wi-Fi turned off), all of them with Google Cloud Messaging turned off. You can see the results in the picture below. Interesting to notice that, despite turning off GCM, Facebook Messaging Lite was still phoning home and receiving messages. Most of my apps, except for a few that need instant alerts, were restricted for background data.
Graphic below showed consumption for this somewhat artificial scenario. Consumption of energy was very low when Wi-Fi is on and set to any of its two modes (flat line between 6h00 and 14h00). Battery stats projected that battery would last for more than 3 days. With Wi-Fi off and 4G on (15h00 to 18h00) battery stats projected that battery would last for 1 day and 3 hours. The two first green bars under “Screen on” represent the time of change of Wi-Fi mode, from sleep to always on then to off. Radio (4G) appears to consume more energy, but I have an impression that Messenger had a role in this significantly higher consumption by artificially keeping radio always on, having less of an impact with Wi-Fi.
Conclusion: use Wi-Fi as much as possible, and “always on” is possibly a better setting under certain use scenarios since it avoids reconnections and doesn’t appear to negatively affect battery.