What is the advantage of the tri-clamp fittings on the conical fermenters that would justify the additional expense?

Tri-clamp fittings are definitely the best kind of fittings you can have; if you go to any commercial brewery or dairy and take a look at what they're using for their connections, more than likely it will be tri-clamp, or "Sanitary" fittings. The reason for this is that you can easily see (and this means easily clean and sanitize) every surface that comes in contact with your beer. In addition they are easy to use, very sturdy and they form an excellent seal which means they never leak.