compare to and compare with is very similar. Chris mentions compare to is used to compare things that are different in nature, while compare with is used to compare similar things. However, people use it interchangeably when writing.
In Chinese translation, I don't think there is a separation of the usage of 'compare to' and 'compare with'.
A compared to B : A 比 B 。。。
A compared to B will be。。。 : A 要比 B ...
Compare A and B: A 和 B 做个比较
comparable: 好比: A 好比 B
A is analogous (i.e. same as) to B last time: A 比照 B 上次
Compare and contrast A and B: 對比 A 跟 B