I looked them up and they both have relatively the same meaning. So what's the difference between the two?
依偎 implies a strong sentimental attachement, usually expressing love or affection. Mostly used between couples, lovers, child and parent.
偎傍 doesn't necessarily carry so much personal feelings, just meaning "stay side by side closely" and is seldom to use in informal/oral conversation. I think it's original from Chinese poems.