If you post your serialnumber I might check the specs of your mainboard.
Whether or not your PC will run better depends mainly on how you use it. If you do heavy video editting it might improve performance. Loading large quantities of data (as in databases) might also benefit. The average user should not be needing that much of memory however.
The question on compatibility is a more difficult one. If you have good quality memory that runs stable and has about the same specs as the original modules, then that should probably run OK. But if you can make a deal with your supplier to return it if you have problems, then I would strongly advise you to do that.