You are in the right size range for your weight but probably towards the lower half of the range. That would make the board feel slightly stiffer for you (as apposed to softer if you were at the top of the weight range). Plus I am sure whatever you rented in the past was not a BTX board so you may have a slight learning curve with getting used to rocker.
Are you falling because it is sliding out on a turn? Or are you falling entering a turn? Or turning at slow speeds?