Extremely high mobile data usage compared to Android

I bought an iPhone 5s 2 days ago (iOS 8.0 12A365 by default). I wanted to migrate from Android to iPhone, but unfortunately I have problems with enormous data usage.

I made a couple of tests. First, my Android phone was connected with Wifi (it measures the wifi data too), while the iPhone had my SIM card in it to be able to me sure the used amount of data. On iPhone Gmail and Hangouts was receiving push notifications, the default mail app's mobile data was disabled. Unfortunately gmail and hangouts is very important, so I cannot just get rid of them. On Android, every of my default services was running: gmail, hangouts, Facebook messenger, Viber, etc. On iOS, only Hangouts and Gtalk was enabled. I leave both phones on the desk for a half an hour without touching them. I received some notifications on both of them. For this example the data used for this was 0.1M on Nexus and 0.7M on iOS.

After I reset my data counters, I ran Hangouts, Gmail and FB messenger in the background. They used 1Mbyte in 10 minutes (measured with stopwatch).

Then I started to measure the amount of data needed for checking a mail or a chat message. On Android opening a chat message from a notification is using ~30kbytes, on iPhone, it uses ~140k (Hangouts not opened in background). Checking manually for mail on Android uses ~20k, on iOS ~120. Then I taught maybe the Gmail app is opening gmail as a web page on iOS and downloads a tons of javascript, so I disabled the data connections for Gmail and enabled for builtin message app, and tried to refresh it. It still result in ~120k (and gmail was working with disabled data connection, so it cannot be displayed as an online web page).

Opening Facebook messenger and checking who is online on iOS uses ~10k of data, but when i started it on the iPhone, it downloaded ~300k of something (yes, on a single start and no, it was not the first time I run it). I can't understand what that could be.

I also noticed the Calendar continuously eating data. For past 6 hours, it downloaded 473k, without I even opened it.

System services are also using data (1.6M for past 6 hours). iTunes-accounts (I hope I translated it correctly) uses 487k, and game center also uses an additional 127k (I never ever opened it).

On my Android phone, i checked the mail and used hangouts regularly, sometimes even Facebook messenger without exceeding my old 100Mb/month limit (about 10 hours on wifi, 14 on mobile data per day in average). For past 6 hours, my iPhone used 8.2Mb of data, without even starting Safari or Viber (with this amount of data usage, even if we 0 data usage at night, there would be ~800 Mbytes data per month).

Is there any way to solve this problem (without using Wifi instead, turning off notifications, etc), or I have to sell my brand new iPhone and continue to use Android? The phone is otherwise awesome, but is unusable for me with this amount of data usage.

Thank you

Robert