First of all keep in mind that all tires of a given size are not the same size. For example most 2.35 tires are actually 2.2. This is done so that the manufacturers can claim a lighter weight for a given tire size. I saw two bikes at the bike store. One had 2.35 Kenda Nevegals, the other had 2.35 Weirwolfs, the weirwolfs were way smaller than the Nevegals.
Second, don't get larger tires then your terrain needs and your fitness level can handle. Larger tires will be heavier, and weight in the wheels and tires is VERY noticeable when climbing and accelerating. I actually just switched from 2.1s to 2.3s and while the traction is incredible it takes a lot more effort to get up hills now.
As far as pros and cons.
For smaller tires
Pros: lightweight so they accelerate and climb better.
Cons: Have to run more pressure so they are less comfortable with less traction. More prone to pinch flats
For larger tires
Pros: Great traction and you can run lower pressures to get some suspension action. Less chance of pinch flats.
Cons: Heavy. Much harder to climb and accelerate. May not fit bike, or properly fit the rims.
There are more pros and cons, but these are the major ones.