I offer my input as someone who went through the JET process (only to get stuck as an alternate
)
I think that an important thing they look for is friendliness and an outgoing personality. I had two friends who also applied the same time as me, and they both made it. I think I was more qualified from the "interest in Japan", academic performance, and experience working with kids perspectives; but they both have more outgoing personalities than me.
Both actually had two years of formal Japanese language study (I had 1) so I think that JET doesn't necessarily discriminate against it.
Ultimately, though, it will vary from person to person and I won't ever know why I didn't make it and they did.
But in any case, from what I've gathered from them, JET is a far better experience than the private eikaiwas on many levels. The pay is better, the benefits are better, and the social circle and support network already in place is much bigger.