A major difference that the hosts recognize as they feature their first female warrior is the way a man thinks and acts versus a woman's. One of the hosts stated that a woman would have been more strategic in battle and to consider that when portraying Joan. From the sources we have read, it didn't seem like Joan did much strategizing or if she did, it wasn't often with other leaders.
Joan's siege cannon that she would have been more effective to break walls and cause more damage than William's Torsion catapult. While the Torsion canon would have been able to cause damage within the walled city and "spread the Bubonic Plague" according to the show, Joan's canon would have been able to weaken the wall itself and go through a humans body with a short reload time. In the simulation comparison, Joan would have won the long range siege weapon.
For Joan's archery simulation, they had chosen the steel crossbow. The reload time for it proved to be unfavorable compared to William's composite crossbow but had more hits, more deadly and accurate. Since the battles would have been during a siege and time wasn't as much of an issue, Joan won the best medium range weapon category.
After doing their best with historians, technology and weaponry experts, the show does the best it can at guessing what would happen. It is all simulated to the best they can do.
Photo Sources
http://img1.wikia.nocookie.net/__cb20130407190444/deadliestfiction/images/6/63/William_the_conqueror.png
http://img3.wikia.nocookie.net/__cb20110902204703/deadliestwarrior/images/1/10/JoanOfArc.jpg
Video Source
https://www.youtube.com/watch?v=PhaTSM9BLvQ