Comparisons of that sort are always difficult.
To start with: comparing a new Pi 500+ with a refurbished desktop isn't fair. One is new the other isn't.
What do you mean by 'equivalent performance'? Most PCs spend most of their time idle. For some uses performance matters, for others it doesn't. I have used a Pi 5 quite a bit, and I find it is sufficiently responsive that I don't notice any sluggishness compared with my (much more powerful) desktop PC.
The Pi uses less power than a PC -- especially when that PC is a refurbished older model -- which is reason in itself to prefer it.
The Pi 500+ has nice mechanical keyboard. My PC also has a nice mechanical keyboard, but that keyboard cost 2/3 of the price of a Pi
500+ all on its own. A refurb PC that you buy for the cost of a new Pi 500+ probably won't come with a keyboard at all.For some of us the mere fact that the Pi doesn't use a boring old x86-64 CPU is reason enough to prefer it over a similarly priced used PC. For some of us GPIO access is important.
The cheapest refurb desktop I can find on Tier1 online, today, is a Dell Optiplex Micro at £299 when spec'd with the same RAM and SSD as the Pi
500+. About 50% more than the Pi 500+. That's a 6-core i5, so definitely more powerful than the Pi. At that price it comes with Windows 10 (or 11) Home so you'd probably want to spend another £20 for the Pro version. It doesn't come with any application software, but Firefox, LibreOffice, Etc. are as free for Windows as they are for the Pi. You do get an audio jack, which the Pi lacks, and can expand the RAM.It's hard to say which is the better value. So much depends on what you want to do with it.