CTRL + W usually deletes everything until the previous whitespace, so it would delete the whole '/var/log/nginx/' string in OP's example. Alt + backspace usually deletes until it encounters a non-alphanumeric character. Be careful working CTRL + W into muscle memory though, I've lost count of how many browser tabs I've closed by accident...
In my terminal it's the exact opposite – Alt-Backspace deletes to the previous space, whereas Ctrl-W deletes to the last non-alphanumeric (such as /). I'm using fish shell in an Alacritty terminal. Yeah, pressing Ctrl-W accidentially is a pain sometimes ... but Ctrl-Shift-T in Firefox is a godsend.
Fun fact: despite having absolutely no menu entry for it, and I believe not even a command available with Ctrl+Shift+P, Vscode supports Ctrl+Shift+T to re-open a closed tab. Discovered out of pure muscle memory.