Why is the amount of time needed to turn the screen on not always the same?
Here are your answers:


Depending on how many of the CPU cores are asleep (clocking at less than 200mHz for your phone), the system needs to wake up those. This takes time.
If the device is not asleep (doing background work), the screen will turn on very quickly.
Best way to deal with: Don't use the power button to turn on the screen, but rather use the Home button. The Home button will not lock your phone and thus pressing it more than once doesn't have an impact on usability.
The hardware/electrical designer will tell you that conserving battery is slightly more important than quick screen-turn-on times. The UX engineer can't do anything about it. Making sure the system runs as it should does not depend on the hardware configuration (most notably the minimum clock rate/time until deep sleep ).
Newer phones may have a better kernel wake-up configuration, that turns on the screen faster (custom kernels for your phone can do that, too), but I can't promise anything.


It's a trade-off between battery and user experience.
I must admit that Samsung's TouchWiz has plenty problems like that one, which led me to switch to custom roms.