New parts, or new pc.

Well what are your current parts and your budget?

Upgrading the parts would be the most cheapest and logical option. Why would you get a new PC?

Yeah I'd just go with upgrading the Video card and CPU unless your motherboard doesn't support new parts or something.

Parts, unless you're using an architecture that is/was End of Life or maxed out.

If you have a 1st Gen Intel or AMD, new computer is the best option 2nd Gen Sandy (if overclocking which isn't needed) CPU + 3rd Gen Motherboard (backwards compatible), 3rd Gen Ivy Bridge Motherboard + CPU, or 4th Gen Haswell (have yet to try myself). You will get at least 60-80% performance gain over 1st Gen as the motherboard is redesigned to have direct access to memory and graphics processing (less bottlenecks). Else graphics card is the biggest bang for your buck... don't go too cheap - Nvidia GTX660 or better.

the best graphics card you can buy without a second generation intel core i3 2000 series or third generation intel core i3 3000 series limiting performance in games is the nVIDIA GeForce GTX 660 for a 1080p monitor. if upgrading to a better graphics card it would be neccessary to upgrade your cpu to avoid a cpu bottleneck. Also make sure your power supply has enough wattage