Although my question is not about difference between definition of entropies, I can still provide a few references:
1. E.T. Jaynes, "Gibbs vs Boltzmann Entropies", Am. J. Physics, v. 33, 391 (1965); doi: 10.1119/1.1971557
2. R.H. Swendsen, J.-S. Wang, " The Gibbs "volume" entropy is incorrect"...