Traditional Grip Pros:
- Very common in Marching Percussion
- Looks 'cooler' (subjective)
- Easy to play on a tilted drum, harder to play on a level drum.
- Easier to play very soft as you are pulling the stick down instead of pushing it.
Traditional Grip Cons:
- Harder to keep both of your Right and Left hand sounding the same.
- Slightly more difficult to learn properly as it involves less common muscles and the motion is awkward to start out with.
- Harder to move around and play different drums.
The pros and cons for Matched Grip are basically the opposite of those for traditional.
I am andan advocate of learning matched first, and traditional later if you need/want to. I regularly play with both and my left hand is equally good in either grip, although it does take some extra effort to keep things that way.
Traditional grip is most commonly used in marching percussion because it is great for playing on a tilted drum (in fact, that's why it was invented). Many jazz drummers use traditional, but I've noticed that most of them switch to matched when they actually need to move around the kit.
It ultimately comes down to what works for you. :D