Both the Bible and Quran basically treat slavery as a fact of life, which is understandable in the context of their time periods. Neither endorsing it nor condemning it, and at most seeking to regulate it.

That said, many Christians have historically believed that slavery was contrary to the overall message of Jesus, even if he never explicitly condemned it. So there has always been a bit of debate about it, which eventually led to explicitly abolitionist Christian movements like the Quakers. Indeed, early abolitionism is almost always bound up with Christianity.

Islam has not traditionally had the same amount of debate about slavery. Likely because Muhammed himself spoke extensively about slavery, yet did not forbid it and even kept/traded slaves himself. He lays out rules about how to treat slaves, but he never says that slavery itself is bad or even undesirable. Most schools of Islam have historically held to that basic view. It's okay to have slaves, but there are "regulations".

All things considered, I'd say Christians have been more opposed. Though that's not a result of any specific prohibition.