I never learned the lyrics to My Country 'Tis of Thee, but I do know the first line (obviously), and so that's what comes to mind when I hear the tune (which I hear a lot during F1 season!). I was given a lyrics sheet for God Save the Queen at my naturalization ceremony, and ... well... those lyrics are rather repetitive and trite*. I remember seeing the words for My Country 'Tis of Thee when I was at camp around age 10, and there was a lot more going on.
I just looked it up... it is repetitive and trite for the first verse. But reading a bit lower, God Save the Queen gets interesting. I particularly like the line "Frustrate their knavish tricks."