I am curious about the differences between Nylon Tip and Wooden Tip. What are the pros and cons of these two?
It really depends on the style of music. If you're playing military or orchestral music, with lots of rolls, you'll probably find a wooden stick rebounds better from the snare drum, making it easier to play.
On the other hand, because wood has a grain, wooden tips give you a slightly different sound depending on the rotation of the stick around its long axis. If you're playing rock or jazz music with a lot of cymbal work (whether it's loud or quiet), you'll find it easier to get a consistent sound with nylon tips.
Nylon tips last longer if you're playing heavily, especially on cymbals, cowbells, or other hard objects you might use to get special sounds.
One more possible consideration is that nylon tips were only invented in the 1950's. If you're playing music that's older than that, you might want to use a wooden stick for authenticity, especially if your audience is close up or you're being videoed.
Nylon tips are good sounding on cymbals, therefore you'll want to use it if you do a lot of cymbal sounds. It is also more consistent than of the wooden tips, since wooden tips will sounds bad when it is depreciated.
Wooden tips on the other hand sounds better on the toms, that's why many rock and pop drummers prefer it than the nylon tips.
The sound is all personal preference, for me personally after a few years of bouncing back and forth between wood and nylon tip I got to where I didn't care for the nylon tips even on cymbals. Nylon tips are brighter and "pingier" (for lack of a better word) on cymbals and eventually I settled on the darker sound from wood tips. Wood tips are also nice because playing the tip and shoulder of the stick on cymbals is more consistent in tone. But it's all about the sound you like.
In terms of durability, both can have issues at the tip. Nylon tips can fall off (but can be glued back on) while the wood eventually chip away over time.
If you're trying to decide on which way to go, then get a set of both and see which one you like best...and to eliminate any other factors from affecting your comparison, try to get the same brand and same model of stick just with a different tip.
In terms of life for the sticks I think Nylon tips generally in my experience tend to drop off the end of the stick, but wood tips tend to chip very frequently leaving sharp edges that have once pierced my snare skin... but as for sound Nylon is better for riding on cymbals and wood tips are better for tom rolls and the like, for metal style music wood tips tend to be used more frequently for blast beats and fast rolls.
As so many people have said, wood tips sound better on toms and snares. That being said, the choice really boils down to the cymbal sound you want and the venue you'll be playing. Large outdoor gig requiring cymbals to cut through? Nylon tips are the way to go. Small bar, or if you're a part of a jazz group or simply want darker cymbal sounds? Wood tips are your best bet.