I do not have any information to talk about the professional level of Gordan Brown, but I think he got that portfolio as a politician not as an economist—not by chance (maybe) he became PM.
In my view, I would prefer a politician as a minister of finance rather than a (nonpolitician) professor, in fact, a strong politician. Of course, I’m thinking for a smart honest politician (do not laugh—some politician can pass this condition). Proposing new policies and getting them passed in parliament and supported by people is not an easy job. A strong political leadership heading a finance ministry would provide an easier job for the head of the government.
So, before looking for a good economist to lead a ministry of finance, first, we should look for someone that has strong political support not only within a ruling party but by people. It would be good to appoint a Nobel Prize economist that on the first day in the job becomes a good politician.