Yes, and the two sides are equal only if a and b are both non negatives, Otherwise, if ab<0 then |a|+|b|>|a+b|

In case someone is not aware of the property, they can do this:

Take x = 0,

Then you have |y| > |z|

Now its clearly seen, y can be lesser and greater than z, since only the absolute of y is greater than z.

Normally, when more than two variables are involved in an equality and you do not have sufficient information to deduce your answer, it is best to try and plug in values and see the answer for yourself. Always start with the simplest values :-
1) Put x = 0, y = 1 and z = 0. In this case, |0| + |1| > |0 + 0| i.e. |1| > |0|. Thus y > z.
1) Put x = 0, y = -1 and z = 0. In this case, |0| + |-1| > |0 + 0| i.e. |1| > |0|. Thus y < z.

Thus, D is the answer.