Berlin was far more prolific than Woody but Woody could be just as trenchant.
Berlin wrote a lot of different songs one that comes to mind is the poignant "Supper Time"
describing a black woman setting the table for her children after hearing that her husband had been lynched.

As to the "rock animus", I don't think that Woody would have liked very much of the lyric content of pop rock. Much of it is just as synthetic as some of the earlier pop music lyrics of the 40's.

I don't hold with the idea that there was a snobbery on the part of these sophisticated
songwriters. I think it had more to do with a dumbing down of musical taste which permeated the pop music field of the 60's and 70's despite the great achievements of Joni Mitchell, Paul Simon and the musical content of a Bachrach. This is to be expected when musical education in the US has been given low priority in the public school system due to
cutbacks by Republicans. It took a long time for "This Land Is Your Land" to catch on because the quality of the song was not recognized for the above reasons. Now every school child in the world knows it even in the US.

I don't agree that the life's struggles were that much different between the two. Berlin came up the hard way as a singing waiter in a waterfront dive in lower N.Y. He was an immigrant from Siberia. The first part of Woody's life were in a fairly economically comfortable environment before the bottom fell out and he took to the road. Both of them paid some dues and I agree that they have a lot in common. "God Bless America" was appropriated by politicians and jingoists that would have made Berlin uncomfortable.
He was grateful to be the beneficiary of the US since he has been exposed to the deprivation of Russia in his time. Woody battled the terrible disease which influenced
much of his life's choices although he had a great social conscience that comes out in his writing.

One of my favorite Berlin songs that match Tom Lehrer's satires is "Pack Up Your Sins And Go To The Devil in Hades".