Moiraine likely knew something of what would happen to her. We know she saw her rescue from the ter'angreal in Rhuidean so it’s possible she also knew that she would die if she resisted. Lanfear didn't have that knowledge but as Deadsy said, the Snakes and Foxes must have a way to contain a Channeler. More specifically, since they enjoy the "taste" of a Channeler it seems likely they might have a specific way to deal with them. Lanfear and Moiraine obviously weren't the first Channelers caught by the Snakes and Foxes.