Suppose we have a surface S (although the question might make as much sense in higher dimensions) and a topological group G. The data of a flat vector bundle on S (up to isomorphism) is the same as a holonomy representation $\pi_1(S) \to G$. For the purpose of defining isomorphisms between flat bundles, we can also think of them in Steenrod's terminology: a flat G-bundle is the same thing as a G'-bundle, where G'=G as a group but has the discrete topology.

Is there a way to tell when two G'-bundles over S are isomorphic as G-bundles (in other words, when are two flat bundles isomorphic without regard to the flat structure)? Conversely, if two flat G'-bundles are isomorphic as G-bundles, does this imply anything about the holonomy maps? Does it matter whether the bundles are principal or not?

Please tell me if I'm confused - the question might be much easier (or harder) than I expect.

Thank you very much!