I don't know why so many people act like GH III is a piece of shit. It's a great game. Is Rock Band better? HELL YES!
However, I feel like if you buy one and not the other you are still missing out. While Rock Band has a lot of good songs, so does GH III. Songs like Black Sunshine, Paint It Black, Prayer for the Refugee, My name is Jonas, La Grange, Before I Forget, Stricken, Cliffs of Dover, Can't Be Saved, My Curse, She Bangs the Drum, Nothing For Me here, and The Way It Ends are all songs that are awesome to play (give or take of course) and warrant a buy.
As far as the DLC goes, the Warner/Reprise pack was NOT that bad. The Linkin Park song is a bit bland (still fun though), but Pretty Handsome Awkward and Sleeping Giants are damn fun songs in my opinion.