The Gibbs update, the elementary update step of the `Gibbs sampler'
(Geman and Geman, 1984; Gelfand and Smith, 1990) is the special case
of variable-at-a-time Metropolis-Hastings obtained by making
the conditional distribution of 
given the rest
of the variables induced by h,
that is, h is an unnormalized version of the proposal density.
If c is the normalizing constant, the Hastings ratio becomes
so the Metropolis rejection step always accepts the proposal.
Like the Metropolis update, the Gibbs sampler has no particular virtues. It too should be used when convenient and effective and not otherwise.