had been supposed to和was supposed to主要是时态方面的区别，前者为过去完成时，后者为一般过去时。另外，前者有时还可表示“本来应该”，相当于was supposed to have done。
关于suppose的用法，本人在金盾出版社出版的《英语常用词多用途词典》上查到了以下用法，本来是摘录下来自己和的，现与你分享：
1. 其后习惯上不接带疑问词的宾语从句，遇此情况，将疑问词移到主句句首：
Where do you suppose he has gone? 你估计他去哪里了呢?
Who do you suppose has stolen the money? 你认为是谁偷了这钱呢?
2. 其后通常不直接跟不定式作宾语，遇此情况可改为宾语从句，如：
通常不说：He supposed to have left his umbrella in the bus.
可改为：He supposed that he had left his umbrella in the bus. 他以为把雨伞忘在公***汽车上了。
3. 后接不定式作宾语补足语时，不定式通常为to be。如：
I supposed him to be about forty.=I supposed that he was about forty. 我估计他大约40岁。
若是to be之外的其他动词，则通常为完成式或进行式。如：
He was supposed to have left for home. 大家以为已动身回家了。
4. 有时可用于引导条件状语从句，相当于连词if，但此时与之相对应的主句通常(但不绝对)为疑问句。如：
Suppose he doesn’t agree, what shall we do? 假如他不同意，那怎么办?
这样用的suppose有时还可用于虚拟语气。如：
Suppose you were given a chance to study in America, would you accept? 假如给你一个到美国学习的机会，你会接受吗?
5. be supposed to do sth为习语，表示“应该(理应)做某事”。如：
They are supposed to arrive before dark. 他们应该在天黑 前到。
Everybody knows, but nobody is supposed to know. 本来谁也 不该知道这事，但人人都知道了。
注：其中的不定式有时可能是进行式或完成式。如：
He’s supposed to be doing his homework at home now. 他现在应该在家里做作业。
He is not supposed to have left the hospital so soon. 他本不该这么早就出院的。
另外，现在分词形式的supposing可用作conj.，表示“假如”，如：
Supposing he does not come, shall we go without him? 如果他不来，是不是不带他去? /
Supposing he can’t come, who will do the work? 如果他不来，谁来干这工作?
这样用的supposing与if用法相似，用以引导条件状语从句，但与之相对应的主句通常(但不绝对)为疑问句。有时还可用于虚拟语气。如：
Supposing there was a war, what would you do? 假如发生战争，你怎么办?
Supposing you fell in love with your boss, what would you do? 假定你爱上了你的老板，你会怎么办?
注：suppose也有类似用法：Suppose [Supposing] we miss the train, what shall we do? 假如我们误了火车，我们将怎么办?