Now here's a good question. Ever since the demise of the gigahertz race, chip designs began to focus on working harder, rather than faster, so the answer isn't immediately obvious. Toss number of cores and technologies such as Hyper-threading into the mix and we have to turn to benchmarks to get a resolution.
Rafael Coelho from Hardware Secrets put together a number of tests to find out if the aforementioned scenario warrants swapping CPUs. Coelho dug up a Core 2 Quad Q8300 from 2008 and benched it alongside a Core i3 4150, Pentium N3700 and Athlon 5150 -- all from mid-2014 / early-2015.
Seven years is an eternity in the CPU business, but you don't need to feel bad if you invested in a processor way back when. While it does get beat in the gaming-orientated 3D Mark tests, it outperformed its up-to-date, but low-end counterparts in PCMark, Cinebench and Photoshop.
A follow-up article by Coelho takes the gaming tests further, with the results showing that if your PC's primary role is for play, it's almost always better to go with newer, low-end chip, rather than sticking with outdated hardware.
Which is the Faster CPU: old but high-end or entry-level and new? [Hardware Secrets]