The population of males is higher than their gender counterpart.
I wouldn't say that this is flat out wrong, but it makes the reader stop and think to understand what is being said, and it feels both akward and pretentious. I would advise against using this.
The population of males is higher than their female counterpart.
This is clearer, but "counterpart" seems to serve no useful purpose except to increase the average word length and falsely suggest greater precision.
The population of males is larger than the population of females.
This is clearer and more accurate. If it is OK to write "males", then it should be OK to write 'females". The parallelism in form emphasizes the parallelism in meaning. "Higher" not as good a way to describe the increase in population numbers as "larger".
By the way, in the example sentences in the question, either "their" should be changed to "its" treating a "population" as a single thing, or else "counterpart" should be "counterparts", treatign it as a collection of people. I would favor the 'its' form.