Welded fittings are permanent, stronger, and leak free. They're generally more expensive, though. They also have that "bling" factor some brewers are looking for, but can also be easily botched by a less-than-skilled welder.
Weldless fittings are completely removable, easily installed at home, and replaceable. They can leak, however, if not properly installed.
That said, I use weldless fittings ... these
fittings, to be exact. Installed into a 7/8" hole, they are perfectly leak free.