Don't forget the lesser-known Texas and alt-country writers
First off, I love Dylan and count Highway 61, Blood On The Tracks, and Desire as three of the best albums I own. I think, however, Steve Earle summed it up nicely: "Townes Van Zandt is the best songwriter in the whole world and I'll stand on Bob Dylan's coffee table in my cowboy boots and say that."
I won't say TVZ or anyone else is "the best" songwriter out there, but I think his songs (esp. Mr. Gold and Mr. Mud, If I Needed You, and Poncho and Lefty) stand up quite well when compared to Dylan, Bruce, Neil Young, or most any popular songwriter. I would also say that about Guy Clark, Steve Earle (I love all his albums, but the post-prison and pre-politics period produced his best writing IMHO), Billy Joe Shaver, James McMurtry, and Robert Earl Keen. If you enjoy Dylan's and Springsteen's folkier stuff and are unfamiliar with any of these cats, pm me and I can recommend specific albums to check out.
Also, many newer songwriters in Texas and alt-country (whatever that means) are writing entire albums that are nothing short of lyrical classics. Chris Knight's first three albums made me claim he is the second coming of Bruce because of how well they captured the haunting nature of The River and Nebraska. All of Uncle Tupelo's albums, as well as some of Son Volt's and Wilco's, are just as good as anything Dylan, Woody Guthrie, and Bruce have put out, at least to the ears and mind of this former rustbelter. Finally, the Drive-By Truckers, whose songwriters have been compared not only to Dylan, Bruce, and Jaggar/Richards by the press but also to William Faulkner and Flannary O'Connor, show that you can write lyrical masterpieces that flat out rock. Check their albums Decoration Day and Southern Rock Opera to see what I mean. Check them out live and you will start claiming that they are the saviors of rock and roll.
OT, but have you all heard Dylan's Theme Time Radio Hour on XM? It's great to hear him play songs that influence him, and surprisingly his voice is perfect for being a DJ.