Personal opinions and general observations:

Pros:

1. Better stability at highway speeds
2. A flat tire is not as dangerous as you still have other tires in use
3. More safety since you have brakes on 4 wheels instead of 2
4. Less prone to sway
5. You track straighter in a side wind and less likely to bounce
6. Can handle a heavier payload
7. Generally tandem axles are farther back on the trailer, so backing up is much easier.

Cons:

1. Trailer will cost more
2. Trailer will weigh more
3. Fuel consumption will be higher due to more weight
4. Higher maintenance costs as you have 4 wheels to maintain
5. Much more important to tow level so tires wear evenly