Muslim historians recorded the Mongol conquest of Baghdad. In order to evaluate potential bias in these records, it would be useful to compare them to other records of Mongol conquests. Since the Mongols didn't record their side of the story, do we have any other, more neutral records of Mongol conquest and their behavior towards conquered peoples?
In Russia Mongols usually demanded the cities to surrender. If a city surrendered without a major fight, the Mongols usually would not conduct much of mass killings. They would impose a heavy taxation and require the city to provide troops for their further conquests.
Other than that they usually did not intervene much in the internal affairs and customs. They did not impose their laws and did not try to win the popularity with the people either.
Particularly since they did not force people to convert into another religion, their conquests were not associated with much of religious bloodshed which accompanied the religious wars of the time, such as the Crusades.
On the other hand if a city would not surrender, they could proceed as far as killing all the inhabitants except a few poeple whom they then would instruct to go to the other cities in the area and spread the word about how the Mongols brutal to those who does not surrender so to advise them to give up without resistence.
Here is an interesting first-hand account of an Armenian cleric who experienced their behavior. Don't know for sure if his account is completely unbiased. Link