Both of your code snippets will retrieve the same value yes (the Z angle of particle "1").
I am unsure about what you mean with "A simple problem is complicated?" but there are many ways to solve problems in programming.
If you really only need the z angle your second version is obviously better as it is both faster to write and to execute (as it will (most likely at least) result in fewer operations).
Vectors are good since they allow you to perform 3d maths, something which might be of use in a more complex application, so there are uses for that approach too, it depends on what you want to accomplish
"Why do programmers get Halloween and Christmas mixed up?"
Because Oct(31) = Dec(25)