Transferring a hard drive to another MacBook Pro?

If the MacBook Pro's are from the same series that shouldn't be a problem.

What can get you if you are jumping across different series of systems is the SATA I/O speed the older drive is likely SATA II and the newer system is SATA III. Then the given OS version, as an example OS-9 Vs OS-X; and within OS-X: 32bit Vs 64bit as some apps may not work and the needed hardware drivers needed for the newer system aren't present.

The best way is setup the systems current HD (not swapping them about) with the best OS for it (if it can run Mavericks go for it) and all of the needed OS patches. Then connect your old system back to back with your new system using a Firewire or Ethernet cable connecting the two systems, then run Apples Migration Assistant application. It will move over all of your stuff and apps for all of your user accounts. Its one of my favorite tools.