@arlawson
The problem you've described ("most of the time my torrent client never uploads after I download stuff.") sounds familiar to me.
I've found that while a torrent is at a seeder/leecher ratio of 1 to any other number (say 1/50 or 1/100) you will pick up lots of leechers to upload to before you've finished getting the file yourself. Once the ratio tips (the moment when more than one person has the entire file) that's when the seeding drastically declines. That's been my experience. It's important to note, that while the uploading may decline, it's still a good idea to seed for as long as possible even if no one is connected to your client (you'll still get bonus points based on time seeding).
As far as piratebay seeming to have more leechers for you to seed a file to, those and other open access trackers can have thousands of leechers across multiple trackers, whereas the most you'd see for a file here on our single tracker would be less than 200 per file, so that accounts for your lessened upload activity here as opposed to there.
I don't think your router has anything to do with it.