From people I've spoken to, I get the idea that most of those competitions are set up for commercial gain - and not that of the songwriter!
But if you're looking for feedback, etc to enhance yor craft, look to things like the annual Barleycorn Songwriting Competition - great environment to showcase, learn, make contacts, etc
http://www.songwriters.co.za/blog/2011/07/barleycorn-songwriters-competition