which is stronger?

carbon is stronger as in stiffer but it will only hold so much stress before it gives and then snaps, resulting in an expensive repair. Plastic will take also only so much stress but it will bend and flex a lot more than carbon so it is harder to break. Also if you put your plastic parts in boiling water for a few minutes it will make them even more flexy so you will break them even less. Rule of thumb if you have a lot of money and do a lot of racing and you are an experienced driver that doesn't crash much and want the lightest parts go carbon, if you just bash and sometimes crash go plastic.

^^ agreed.

Carbon fiber has a very high compressive strength, but a fairly low tensile strength. and it has basically NO modulus of elasticity, so as soon as it has been sterssed past it's yeild point, it will snap.

Whereas plastic has a lower compressive strength and a similar tensile strength to carbon fiber. But it has a greater modulus of elasticity, so when it is under stress it has the ability to stretch or slightly twist without breaking.

here is pretty much how it works, I dont remember whre I read this though.
Most new people get graphite or carbon fiber parts after they break there stock parts so that they dont break the parts again. However, they are more likely to break when the have carbon fiber or graphite because they are more brittle. The reason why good drivers have graphite and carbon fiber parts is because they are light, and make the car more responsive, so they crash less. But, if they do crash, the chance they will break something will be higher because the parts dont bend like the stock parts do. also, the carbon fiber parts cost a lot more to replace than the stock plastic.