I already "own" the first Beat Hazard on Steam and I'm thinking to get a DRM-Free version on gog, but before to do that I'd like to know: Are there any significant differences between the two versions or are they the same ?
In particular, are the Gold ships a Steam exclusive or are they in the gog version as well ?

This is the definition of a necropost, but for what it's worth, the answer is no, the versions are not the same.

You do get the Gold and Mini Gold ships on the GOG version, straight from the get go.

However the GOG version is completely missing some features (online multiplayer and ship creator/workshop are the most serious in my opinion), and the developer seems to be mostly done with the game aside from the occasional bugfixes, so I don't really see this changing. Definitely could be done, just seems that the will is not there.