Can anyone really answer this question but you?
I can tell you that the pickups in the S320 are not known as the best around. If you go for the S, maybe try some DiMarzio Paf Pro's. They are great in mahogany, and cover the hard rock/metal stuff no problems.
Another factor in the SZR sounding "rich and gruntier" is the shorter scale neck. Typically 24.75 scale guitars sound a bit "meatier" than 25.5 scale guitars like the S series.
In the end, it's you that will play what you buy, so it's gotta be you who decides.
Hope this helped you make your mind up.
Rock on!