This really depends on your residency status and whether any reciprocal healthcare agreements apply between your home country and destination — that changes what you're actually entitled to under the public system, sometimes substantially. The Health & Insurance section of your destination's guide should clarify what applies specifically to retirees/pensioners, since eligibility rules there often differ from working-age residents.
Generally, private supplementary cover is worth strongly considering if you have any pre-existing conditions or want faster access to specialists, even where the public system is genuinely good.