The difference between "-에 비해서" and "보다" is equivalent to the difference between "in comparison with" and "than".
"보다" is a comparative particle, and "-에 비해서" is a phrase, showing for "comparison", like a prepositional phrase in English.
이것보다 저것이 더 크다. This is bigger than that.
이것이 저것에 비해서 더 크다. This is bigger in comparison to/with that.