Locked camera is, for the most part, a beginner's thing. A movable camera is great but takes some getting used to, much like smart casting.
Locked camera and a lack of smart casting are the two major mechanical differences that I see between beginners and veterans.
For pros and cons:
Locked camera:
Pros:
You won't lose yourself in a teamfight
It makes the controls simpler for when you're first starting out
Cons:
It severely hampers your awareness, meaning if something isn't on your screen, the only way to see it is the mini map, which is also an adjustment for many new players.
Movable camera:
Pros:
You can look at anything you want.
You can check lanes for ganking opportunities, see if anyone is in trouble for teleport/shen ult etc, check dragon, check baron, check your team's wards, look down your lane etc.
Cons:
You'll occasionally lose yourself in a team fight if it is particularly hectic.
It is one more thing to control for new players.