Why hasn't anyone ever mentioned this module? As in I've read nearly every node to do with parsing on this site for the past 3 years and I've never heard of it.

A quick check with Super Search shows that it has been mentioned here before.

Would I be correct in thinking that the following are equivalent?

To be honest I'm not 100% sure. I expect that there are corner cases where Text::ParseWords doesn't do the right thing and one of the other modules does. But I've never come across one of these cases.

I should point out that in DMP I discussed Text::CSV and not Text::ParseWords because, like you, I hadn't seen Text::ParseWords at that time. It seems to be a very underused module.