If you have a 64-bit OS, you could see some benefit in adding RAM. On my Win7 and Win10 machines, I have noticed as much as 75% RAM utilization when sitting idle or doing some light browsing. On my workstation with Win10 I have 4GB of DDR3, and it runs just fine. My Win7 daily driver has 8GB of RAM. Otherwise they are the same hardware. Each boots from a recent model SATA III SSD, each uses a separate HDD for bulk storage, they are each running an AMD FX-8350 processor, use the same model memory sticks, and neither is totally loaded down with superfluous software. They "feel" about the same in general use, but any heavy use (thirty tabs open in Chrome) seems smoother on the Win7 box with 8GB.
I would venture to say you may well notice an improvement in your computer's operation if you add memory. Others may not agree with me, but you know what they say about opinions...
Absolutely, to give a definitive answer I should try them both with the same amount of RAM, and each with 4 and then 8GB, but I don't fiddle with the hardware unless it's a periodic cleaning or something lets out the magic smoke.
Oh, and +1000 for an SSD upgrade from that ancient spinner. You will absolutely feel a difference with an SSD. As a matter of fact, you will see a very nice improvement if you do both the RAM upgrade and SSD install.