Hey there,
No, older gen won't make much of a difference. More often or not it comes down to the OS for general lag/unresponsiveness. If you don't re-install windows every year or two, it just bloats up with files, drivers, software etc. The system can feel really laggy. For an easy fix, I'd re-install Windows which would be pretty snappy then.
Your CPU/GPU are getting on, but are still very relevant. If you haven't already, you might look at re-pasting thermal paste on your CPU, check that all your fans are clean and running okay. Some simple PC housekeeping.
You can run programs like HWMon/info to watch your hardware on the fly. This might indicate if there are Hardware issues.