Einstein definitely preferred a close universe in the spirit of Mach's principle, In both an open and closed universe, there must be boundary and/or initial conditions, but, the question is if the distribution of mass-energy is sufficient to fully define the field, or if independent boundary conditions are necessary to seal the deal. In a closed universe boundary conditions can be clearly defined by the mass-energy distribution, but, in an open universe they are quite independent. Therefore a closed universe can satisfy Mach's principle, whereas an open universe definitely cannot. Of course the relevance of this hinges on the validity of Mach's principle. Since we can regard a field as an actual component of the universe, and given spacetime itself is a field under GR, one can argue Mach's dualistic view is irrelevant. However, the devil is in the details. If the distribution of mass-energy plus boundary conditions at infinity yield a unique solution - and which they do under Maxwell's equations (which are linear), but do not under Einstein's equations (which are non-linear). This is probably the point made by Misner, et al, when they comment that "Einstein's theory...demands closure of the geometry in space ... as a boundary condition on initial value equations if they are to yield a well-defined (and, we now know, a unique) 4-geometry".
