Karloy,
It is possible it is power related but the description/symptom is quite general so difficult to say.
Does the application a lot of data to send i.e. it is queued in the system and as a result the LTE connected device is sending faster. You cannot use the SAR backoff for this sort of thing, in fact if the unit is on LTE it has to control the power independently as it has certain power obligations to meet. The way to eliminate whether LTE is a factor or not is to turn it off with at!selrat and just have the unit on 3G.
From the description it is unlikely the networkhas anything to do with it, one comment is quite telling though ad that is that you have good signal strength, the implication of this is that the transmit path is fairly clear as well meaning that it should not be transmitting at full power which is where the huge power cinsumptions come in in addition to high data rates.
Would be good for you to send a few commands to the unit to get some context/background information.
ati
at!gstatus?
at+cgdcont?
at+cimi
at!priid
Regards
Matt