Well, totally different roles. Spacek played a young teenage girl on the verge of marriage. Harris played a girl stuck in an earlier age and quite the tomboy. Harris' character was younger.
Harris was more convincing as an adolescent, but both were superb.

This is a good point, they were both so exquisite in these juvenile roles. This is the youngest I've ever seen Julie Harris. I saw her in East of Eden, which was three years later, and appropriately enough, she is finally playing a teenager in that. But considering Sissy Spacek was 31 when she did Coal Miner's Daughter, and even 27 when she did Carrie, playing a wounded but naive high-schooler, I would give the edge to Spacek. The modern-day version I suppose would be Amy Adams, though she doesn't play adolescents.