We have both the Polaris Ranger 6 wheeler and the Mule 3010 that we keep in Garwood (ie; rice fields with mucho mud). The six wheeler is definitely better in getting you just about anywhere. Plus with the six wheels, going over rice levees is much easier, virtually impossible to high center due to the extra axle. In six years, I have stuck it twice but anything would have gotten stuck in those conditions. The only drawback to the sixwheeler and wet conditions is the extra maintenance you have to perform. We have to grease all axles and wheels every ten hours. This is an older model so can't provide info on if this has changed on the newer models but read the manual carefully as ours clearly states that in normal driving conditions maintenance can be done every 100 hours. However, in the fine print it clearly states that in wet, muddy conditions the maintenance must be performed every ten hours.
I have only stuck the Mule once but again, anything would have gotten stuck. We drive through mud and water all the time both work very well. Bottom line, in the majority of situations, both will work but if you get into deep stuff with no real bottom then you are going to get stuck. We like the mule since it has the two seats plus bed so we can carry more people and still haul our hunting gear but we use the Polaris when it is super muddy. We also have the lift kit with the large tires on the mule and that really helps with the mud. I, personally, would not buy the mule without the lift kit, it really provides significant additional clearance.
We also have the mule with just the two seats with a high rack and lift kit at our ranch in south texas. We have gotten it stuck but we were able to push out.
There is less standard maintenance required on the Mules. PM if you want to talk further. Hope this helps.