Given it's illegal most everywhere, data is hard or little to come by.
There are two large groups: one with a pretty 'dirty' record regarding abuse/child marriages and another with a clean record. So this could come down more to an environment/community issue than a polygamy issue where, in one community/environment, abuse and child marriages are largely the norm and the other it isn't.
Warren Jeffs' Fundamentalist Church of Jesus Christ of Latter-Day Saints && Apostolic United Brethren. The former having the bad record and the latter having the clean record. (&& being the separator to avoid confusion) The former is larger than the latter but the latter is the second-largest church that practices polygamy.
E:
The burden of proof is also on you to prove that polygamy leads to abuse/child abuse as you are the one making the claim. Given there's little/no data to support either side, you'll have to wait for more research. Which would likely involve legalizing the practice and conducting studies.
There are two large groups: one with a pretty 'dirty' record regarding abuse/child marriages and another with a clean record. So this could come down more to an environment/community issue than a polygamy issue where, in one community/environment, abuse and child marriages are largely the norm and the other it isn't.
Warren Jeffs' Fundamentalist Church of Jesus Christ of Latter-Day Saints && Apostolic United Brethren. The former having the bad record and the latter having the clean record. (&& being the separator to avoid confusion) The former is larger than the latter but the latter is the second-largest church that practices polygamy.
E:
The burden of proof is also on you to prove that polygamy leads to abuse/child abuse as you are the one making the claim. Given there's little/no data to support either side, you'll have to wait for more research. Which would likely involve legalizing the practice and conducting studies.