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.
Here is a understanding:
依偎->weak 依偎 strong 偎傍->have same strength
for example, 依偎 is used as a baby(weak in strength) 依偎 his mother (stronger in strength), and 偎傍 is used as two comrade(have the same strength) 偎傍 each other. There is more example, '杨柳依偎磐石'，'磐石相互偎傍'.