Can you be more specific about the kind of work you want to do? Do you want to work in a psychiatric unit or with general medical patients? When you say "outpatient" do you mean having a clinic or doing things like IOPs/PHPs? Do you want to do any teaching or research? Which is "better" boils down to hard-to-predict factors others have already mentioned like salary, benefits, academic affiliation, patient population, position structure, etc.
Another factor to consider is how you would fit into the system. Private healthcare organizations differ a lot in how they use psychologists. In general, the VA places many psychologists in direct care roles (eg, as providers of psychotherapy), whereas hospitals often favor nurses or social workers for similar roles. Any given VA hospital will have multiple psychologists whose roles are relatively established, whereas at a private hospital, especially a smaller facility, you might be the only psychologist or one of a small few. Your colleagues may not know much about what a psychologist is or is capable of doing. In short, psychologists are well integrated throughout the VA system, whereas they are "square pegs" in many private healthcare organizations (this is changing, but slowly).