The Old Left were intellectual revolutionaries and traditionalists about sexual morality.
The New Left are intellectual revolutionaries and sexual revolutionaries.
(Well, that was how it started-out; but the Old Left became the New Left - and the New Left have dumped intellectual revolution whenever it comes into conflict with sex.)
The Old Left were quite often Christians - in England, especially, they were often strict and ascetic, often Nonconformist Protestants (e.g. Methodists and Quakers) - who eschewed luxurious living, were often teetotal and/ or non-smokers, worked hard, were strongly against gambling, were honest, and were altruistically public spirited.
This was the tradition of Christian Socialism and Ethical Socialism - people such as Fabians Sidney and Beatrice Webb (dishonest, however, when it came to the USSR), economist RH Tawney, Prime Minister Clement Attlee or social scientists such as my old friend Norman Dennis.
(Ex-Mormon) Philosopher Sterling McMurrin was of this type - a Liberal who served in the Kennedy Administration and supported the usual fashionable Lefty causes; his personal sexual life was apparently very traditional and maintained along strict Mormon lines.
An Old Leftist would preach and live intellectual revolution - he was a professional heretic; but would support laws and practices of traditional sexual and social morality - plain living, self-improvement, being useful.
But this kind of Old Leftist is now very rare, almost extinct - and has been replaced by the New Leftist.
The New Left (some of whom were around a long time ago) can be distinguished by their 'Bohemian'/ scoundrellish lives of sexual license - 'open' marriages with extra marital relationships, lovers and mistresses; multiple marriages; non-married partnerships; exploratory and non-heterosexual sex, and so on - including the likes of Bertrand Russell, Fabians such as HG Wells, Hubert Bland (mega-unfaithful husband of writer Edith Nesbit), Margaret Mead, Sartre, Foucault and pretty much all of the nineteen sixties and post-sixties counter culture leaders.
Such people preached sexual revolution, and they lived sexual revolution; and it is hard to avoid the conclusion that they preached sexual revolution mostly because they personally wanted to live that way.
And they often strikingly dishonest, deceitful and exploitative in their personal lives - as inevitably seems to happen with people who focus their lives around quantities of extra-marital sex. They may get a pseudo-honest reputation for confessing their sexual adventures - but only because they are putting them forward as revolutionary virtues.
In general, therefore, it is sex that distinguishes the Old and New Left.
If in doubt - look at the sexual behaviour, and you will see what kind of Leftist you are probably dealing-with.
In terms of motivation, it looks as if the Old Left were sincere in their intellectual revolution lived by it, put that first; and that is what they really wanted more than anything.
In terms of the New Left, it is apparently sex they are most sincere about; and for the New Left, politics is a vast rationalization of sex, and the revolutionary intellect is something which must be bound and muzzled whenever it threatens to constrain their sexual appetites and preferences.
Despicable as are the New Left compared with the Old, the Old Left as a whole did not emerge well from the sexual revolution. The Old Left simply became the New; and - while there were some who withstood sexual temptations - there were very few of the Old Left who remained anchored by their 'puritanical' principles when the tide of the sexual revolution began to rise about them.
Most of them pretty rapidly cut their chains and began to join in the carnivale of sexual subversion, boundary-transgression and inversion of morality as best they could - and to demonize anyone who raised any objections to the abolition of traditional morality.
When it came down to freedom of sexual expression versus freedom of intellectual expression on the Left - sex won; and with barely a struggle.
I suppose there must, somewhere, be an example of a prominent New Left political activist who has retained the traditional morality of the Old Left - A New Leftist who was or is, lived or lives, and publicly defends and advocates traditional marriage and family sexuality...
I just can't think of anyone offhand.