  We consider H\"older continuous cocycles over an accessible partially
hyperbolic system with values in the group of diffeomorphisms of a compact
manifold $M$. We obtain several results for this setting. If a cocycle is
bounded in $C^{1+\gamma}$, we show that it has a continuous invariant family of
$\gamma$-H\"older Riemannian metrics on $M$. We establish continuity of a
measurable conjugacy between two cocycles assuming bunching or existence of
holonomies for both and pre-compactness in $C^0$ for one of them. We give
conditions for existence of a continuous conjugacy between two cocycles in
terms of their cycle weights. We also study the relation between the conjugacy
and holonomies of the cocycles. Our results give arbitrarily small loss of
regularity of the conjugacy along the fiber compared to that of the holonomies
and of the cocycle.
