Crew members will aim to surrender in combat if they reach a panic state. The chance for a surrender is not based on which side has more crew members attacking or defending, rather a chance for a surrender is rolled each time a crew member gets hit by a bullet. Getting hit often and losing health will make it more likely for the crew member to surrender at some point.
Each crew member have their own individual surrender rate, which is based on their traits, attributes, and current health. A hero will be much more unlikely to surrender, while a wimp might surrender immediately.
To find out the surrender rate for a crew member check out their overview tab in the character information. Hovering over the surrender rate will show what is affecting it.