Turntables
Pros:
Cheaper,
Get the real feel of the vinyl,
Some remixes only come out on vinyl,
You learn certain techniques that can only be preformed on a turntable
Cons:
Bigger than CDjs,
Vinyl can be hard to find/expensive,
Not as easy to use as CDjs/less features,
Broken needles can be expensive
CDjs:
Pros:
Use cds (allows music to go from computer to CDj almost instantly),
Cd's are cheaper than vinyl,
More portable than turntables,
Many features that make mixing easier ("hot cues"),
Looks nicer *my opinion only

*
Cons:
Much more expensive,
Can't "scratch the vinyl",
Can't do some turntable moves
When it comes down to it though, I think CDj's are better, even though they're more expensive, they're worth it. Besides, nowadays, if u actually start Dj'ing clubs, most of em have CDj's, so starting out with CDj's is pretty much the future, if u can afford them.