The answer will depend on what you want to do with your new computer. From a strictly speed of executing instructions pov, you may see a 2-3x increase. That's if you run the same software. Can't give a precise answer because your old system may be tuned for running what's on there now. New software is bloated; new OS's are bloated if Apple or MS. If you plan on making movies, doing lots of graphical rendering, etc. the new machine is not enough. Think 4 core, 16-32 GB memory and 1 TB HD. It is probably OK for game play depending on the graphics card.
If your old machine can be upgraded to 4 GB of memory, it will probably run at least 2x faster.