H+ only means that you are using the HSPA+ wireless spectrum. If you were using LTE before, then there might be something else eating your battery life other than data.
That H+ icon means that your phone is connecting to a 3.5G or HSPA+ network through the GSM antenna of your phone. This type of connection is a power-intensive process, consuming more power than connecting your phone to a WiFi network. The power consumption will even be worse if your phone is kept in a place with poor network coverage, since your phone will either be exerting more effort to connect to the cellular site or be attempting to connect to a different cellular site.
To conserve battery power, try connecting to a WiFi network as much as you can. Of course, you can always keep your phone plugged in as much as you can when you don't have access to a WiFi network, e.g. to a mobile battery pack.