Battery drain when wifi is off
Activating the 2G only option solved the issue, indicating a problem with the connection, as mentioned in the comments. 

Another thing that solved it (temporarily, until I install more apps I guess) was reinstalling the OS. I only installed few apps and the minimal PA Gapps package (contains only some indispensable apps by Google), which presumably reduced the amount of background data send. Overall battery consumption with 3G enabled is way lower than with only 2G before.

I've also updated the radio firmware, though I can't confirm if it had any effect. It still seems to switch a lot between E, 3G, H and H+ but without any actual data traffic there is no noticeable impact on battery life.

Another suggestion I've found online somewhere is to use an app that switches to 3G only when particular apps like the browser is used and switches back to 2G otherwise.