Health-NHS
There are now four different NHS systems operating in the UK since devolution, according to health chiefs.
Patient groups said the situation was breeding envy.
Ms Morgan, whose organisation represents NHS trusts and health boards, said there was no longer a universal system across the UK, as there had been when it was set up by the Atlee government in the summer of 1948.
England - NHS market created whereby hospitals and community services have to compete with the private sector for patients, resulting in big falls in waiting times.
Scotland - Doctors have much more of a say in services, with limited involvement from the private sector. Meanwhile, patients enjoy free personal care, unlike the means-tested systems elsewhere.
Wales - Close working relationship between the NHS and local government, which has meant more innovation on public health, but less emphasis on waiting times.
Northern Ireland - Somewhat hamstrung by political situation, but re-organisation of trusts pushed through and good integration between social care and NHS.
In Scotland, where people have been given free personal care - unlike the means-tested systems elsewhere - Ms Morgan said there has been much more consensus.
She described the approach as the "collectivist model".
And in Wales, which has received praise in England for introducing free prescriptions, she said the close working relationship between local government and the NHS had had an impact on public health.
She said it was too early to say which was more successful and in the coming years the differences would become even "greater".