I think this entirely depends on your personal preferences and what private hospital it is, maybe doing some research into the private organisation and the general vibes of the nhs hospital you've applied for would be beneficial? Like looking at the employee reviews on glassdoor, asking around with people that work in the trust/health board, reading the inspections by regulatory bodies (like the CQC rating if you're in England).
Experience is useful, but the day-to-day experience of working there is important too. It really depends on what you care more about at the end of the day.