It has been shown that anything we can't get always seems better than (what) we have owned.
先分析整体结构,其实It是整个句子的形式主语,句子的真正主语是that anything we can't get always seems better than (what) we have owned这一部分（主语从句）,也就是说有这是一个由that引导的主语从句；
再分析这个主语从句里面,主语是anything,而we can't get是anything的定语（定语从句）,what we have owned 则是宾语,是一个宾语从句,这个宾语从句里面缺少宾语,所以用what引导,what充当owned的宾语.
句子结构可以这样：
It has been shown [that anything (we can't get) always seems better than (what we have owned)].
后面那句That we can't get always seems better than (that) we have owned.我怎么看都好像有问题!