Following the female line is more likely to be accurate, without any 'mistakes' regarding paternity. I have come across reports where the percentage of named fathers who are/were not in fact the biological father was said to range between 10% and 15%.
I'm sure you will be able to find examples online.
I first heard of it many years ago in 'nature' programme about sparrows where they said male sparrows often play away while another female's mate is out of sight (maybe doing the same with another female sparrow?). The naturalists said the number of sparrows rearing the resulting chicks that weren't their own was about 12%, and they added as an aside that the rate for humans was roughly the same.