I agree with you on this point, however it should be pointed out that the MUTOs attacked anything that got in their way or that had a nuclear power source, whereas Godzilla seemingly had a singular mindset to destroy the MUTOs and actively avoided causing unnecessary harm.
Remember that he allowed an entire U.S. Naval Battlegroup to go alongside him without harming them, even going so far as to submerge and swim underneath them when they were in his way. Of the three ships that he actually damaged when coming on shore, only one was seemingly in real danger of capsizing. Also, when he first made landfall and the rooftop soldiers opened fire on him, he just ignored them. Old Godzilla would have smashed and/or burned them to ashes (much like that MUTO did at the docks).
The MUTOs, however, seemed to have a "wanton destruction" mindset to them. Disregarding the EMP attack (the purpose of which would be completely unnecessary back when they roamed the surface of the Earth as there were no electronics, but I digress...), they seemed to take a proactive role in the destruction of buildings, personnel, and materiel. Nuclear subs, power plants, and weapons I could understand, as it was a food source, but they actively attacked anything in their way.
The best description I can give to the two sides of this conflict is that the MUTOs were terrorists, whereas Godzilla was a soldier. The MUTOs targeted everyone, but Godzilla only targeted the MUTOs. In war, collateral damage is unavoidable, especially when you are that size.