In some ways, Ayn Rand’s ‘Objectivism’ and Epicureanism have much in common. They both see no value in religion (in terms of human happiness) and they frame happiness/pleasure as the goal of human life, although they differ fundamentally on how to attain it.
For Rand, happiness is born of productive achievement, ie making and selling a product or service. Classical philosophy would criticise this on the basis that his made her happiness a hostage to others and to fortune, lessening her control over the circumstances engendering happiness. An Epicurean would simply state that she simply regurgitates the otherworldliness and heroism of older schools and religions in a new, albeit esoteric form. Can Atlas ever be happy?
‘Atlas’, he who shoulders the burden of the world on his shoulders, is Rand’s superman and he is the only one who can be happy. She is perhaps a Jansenist of a materialist age, for whom ‘narrow is the way that leads to life’ (Mt 7.14) which few attain. The rest of us are presumably cast into where there is weeping and gnashing of teeth (such as in the current USA).
An Epicurean would diagnose Rand’s malady as pursuing an unnatural and unnecessary desire which admits of no satiation. As Wallis Simpson said, ‘You can never be too rich or too thin.’ In such cases, the desire for a useful tool such as money becomes an end in itself. Money is not to be despised - the disciples of Epicurus are not disciples of St Francis - but, as with all unnatural and unnecessary desires, there is always the danger of idolatry and misery. With such desires, the human instinct for hierarchy inserts itself, inspiring the most tortuous efforts to excel in what, at best, is surplus to happiness.
Why does Rand pursue this path? It perhaps stems from the mistaken notion that happiness must be hard-won to be real, restricted to the ‘saints’ and ‘elect’. Today’s prosperity and abundance should make a happy life easy to pursue, freeing us for leisure and ease. That would be too easy, however. Instead, too great a faith is placed in things secondary or tertiary to happiness. Again, faith is placed in the ‘next world’, rendering today the slave of a tomorrow that never comes. Too often, much is never enough - more is always tempting.
Rand’s own life suggests the truth of this. Her private life was unsettled, encompassing a number of affairs with her much younger protégés such as Nathaniel Branden and George Saunders (the latter seventeen years old at the time of the affair with the pension-aged philosopher). She also claimed social security in apparent contradiction of her principles, suggesting (whatever the reason she did so) that her worship of money had not even allowed her to retain her self-respect in old-age.
Despite her protests, Epicurus’ thought represents an easier, more level and more open path to tranquility and happiness. Again, money should not be despised, but it should be seen and valued as a tool for eliminating disturbance in one’s life and maintaining a suitable degree of simple comfort. Rand achieved none of these things, her desires (both natural and unnatural) remaining unsatiated, even at the time of life when they abate.
‘Call no man happy until he is dead’, said Aristotle. Rand was never happy, alive or dead.
Rand makes money the end of life, and hates pleasure. She also inspired many awful ideas, like the deregulation of the financial industry which led to the 2008 financial collapse (the FED leader Greenspan had been a direct disciple of Rand who studied at her feet at one point, and had been implementing her ideals). During this financial collapse, Americans lost over 40 % of their life savings to the wolves of Wall Street. Randian ideology favors the billionaires and this is why they are trying to advance it, but the average person will be made miserable by this.
As you said, Rand herself could not live up to her ideals, had to "mooch" off the government towards the end of her life, and was unfaithful to her husband with one of her disciples, who later betrayed her for another woman, and this scandal was quite public and showed how unhinged, unprincipled, and unhappy she was.
With his defense of science and the social contract in Kyriai Doxai, I think Epicurus is a better defender of Western liberal values.