You have to remember, we have no idea what your skill level is, and how much trouble shooting you've done to isolate the problem, so don't get upset that we have to ask you questions like these. This is what you get for free support via a forum!
IMO, Transmit is an excellent FTP app. It's worked very, very well for me for years, so the problem isn't FTP on the Mac, nor is it FTP clients on the Mac. it's something about your set up that will take some time to work out the problem and solution.
Does your site expect to use passive or active FTP? What was the setting on the PC? Have you tried to switch to active since you seem to be using passive?
Also, consider asking for an ssh connection instead. I don't know how much you know about FTP, but it sends your username and password in cleartext and it's pretty easy to sniff that out. FTP has been very much deprecated over the years..