Usually i would be EARNED or RECEIVED a doctorate. As to your question, there's no real difference.

Both sentences convey the same basic idea: that the person obtained a doctorate degree from the University of Zurich. However, there is a subtle difference in emphasis between the two sentences. "He gained a doctorate from the University of Zurich." This sentence emphasizes the act of obtaining the doctorate. It highlights the achievement itself and the fact that the person successfully completed the requirements for the degree. The focus is on the individual's accomplishment. "He gained a doctorate at the University of Zurich." This sentence emphasizes the location where the person obtained the doctorate. It highlights the specific university where the degree was earned. The focus is on the university's role in conferring the degree. In summary, the first sentence emphasizes the achievement, while the second sentence emphasizes the university where the degree was obtained. The difference is subtle and both sentences are generally interchangeable in most contexts.

The first answers the question "at which university did he study?" or "which university gave him his degree?" The second answers the question "where did he study?" But, really, there's not much difference. "At" is a preposition that specifies "where".