I think it comes down to if you know the unit well or not.
The advantage of 4th is that it is closer to the peak breeding time than 3rd, so most all bucks will be with does. During early in the 3rd, the bigger bucks might not yet be with the does. The 2nd advantage is that the later dates give you a better chance at weather helping either bring bucks down (concentrating the deer) or get them moving more during the day. The 3rd advantage is the number of hunters, probably only 10% of the amount hunting during 3rd.
The cons of 4th are you only have five days, so if you don't know the unit well then you could be in big trouble as it will likely take a few days to the whole season to learn it. It is hard to scout it as there are only 2 days between 3rd and 4th. You might want to scout it right now or the year before you hunt it. The last disadvantage is that the 5 vs. 9 day hunts, there might be a better chance to get a few prime hunting weather days during 3rd than 4th just because there are twice as many hunting days. This is unit specific, but it is possible that most of the deer might have moved through public onto private by the time 4th season rolls around and then you could be in trouble. The last advantage to 3rd is if you get an early snow, they could be concentrated down lower and you get to hunt them before 4th starts.
I am guessing your brothers killed their bucks during 3rd season, could you draw a 4th in the same unit and use their intel to give you an advantage? If they killed them in 2nd in a better unit, perhaps you could draw 3rd season there?
Where you are sitting, you could either hunt one of the more premier units during 3rd season or 2nd or a 4th season hunt that is easier to draw during 3rd season. Tough decision because the 4th season tag you can draw might have got blasted with hunters during 2nd and 3rd versus a harder to draw 3rd season tag that didn't receive as much pressure. Either way there are no freebies to shooting a big mule deer, have to hunt smart and hard.