When I used Path Finder, I used it as a Finder replacement. "Open in Finder" opened Path Finder. I replace Finder's desktop with Path Finder's. I never saw Finder at all. You can even tell Path Finder to prevent Finder from launching. I never bothered with that since I thought it might be a good escape hatch if Path Finder didn't satisfy my needs for some particular thing.
That is important if you have a large archive and just want to grab some files from it or see what it contains without having to expand the whole thing. Windows Explorer provides this. On the Mac I use BetterZip for that. It would be nice to have that directly in Finder.
I've not really explored the limits of Finder; I've only ever connected to simple file shares (smb protocol). I know that ForkLift offers much more. I see the options of SFTP, FTP, FTP TLS, WebDAV, WebDEV HTTS, Amazon S3, Backblaze B2, Google Drive, Rackspace CloudFiles, SMB, AFP, NFS, and VNC.
Occasionally I've found that Spotlight refuses to find the file I'm looking for or gives me too many irrelevant answers. I know there's a full query language but I haven't really learned it. There is a tool that is a graphical front-end to Spotlight, but I can't remember it's name.
I sometimes just have better luck with a third party tool or the terminal (using grep/find). When I really need to count on finding things, I keep them indexed in DevonThink. That company also has EasyFind which assists in searches. I would appreciate a more sophisticated search that has a shallow learning curve built right into Finder.
If Finder provided dual pane, I would just stop looking for a Finder replacement. This is the one feature that I really want. I'm so often opening multiple finder windows to copy or just look in two different places at the same time. When I used Path Finder, and when I use ForkLift now, I really appreciate have two panes. I guess the importance of this one depends on how often you are using two windows.