Pros:
Space, Space, Space and more Space compared to on property (multiple bedrooms and bath)
Full kitchen - can choose to cook or not cook as much as you want. Less eating out (saves money)
Washer/Dryer - no sharing and not coin operated
Multiple TVs, games and entertainment system
No sharing of WiFi with 100 others around you
Feels more like home, than a hotel room
More flexibility in traveling around the resort. No need to wait for Disney transportation.
Cons:
Transportation - will need a car to drive to/from WDW & airport. $15 p/day to park. Can use Disney transportation once there. (There is a shuttle service available, but pickup/drop-off are scheduled, like 2 in am & 2 in pm)
No full Disney immersion
No delivery of purchases of souvenirs to your room
No Early Magical Hours entry
No other perks like FP+, for resort guests only
Have to go shopping if you plan to cook
I think that the pool issue is a bit of a wash.
I believe that it comes down to the type of experience you want and your budget. My family has stayed both on and off property. Like both, for different reasons. If you want the full Disney immersion, then on property is the way to go. You can find plenty of places in WH that are decked out Disney, but not quite the same as being in the park.
For me it usually comes down to money. I look at cost of staying on property with dining, and then do the math for staying off property. We usually drive, so the car is not a factor. I have found it usually cheaper to stay off site than on. But that depends on if Disney is offering
free dining, room discounts or military discounts. How much you eat out vs. make.
Good Luck!