How do you decide whether to use "-ing" or "-ation/-age" when either is correct?

"The demonising of people on benefits by the Government is shameful"

"The demonisation of people on benefits by the Government is shameful"

And by the way, should I be saying "either is correct" or "both are correct"?

Other things being equal, choose the gerund

If both are correct*, I would decide on the basis of “familiarity” and number of syllables. Familiarity (not frequency) is subjective, but if neither seems strange (as here) I would always go for the shorter — “ing”, rather than “ation”. It is also more English, and less Latin.

I forget who devised this “rule” — familiar, short, Anglo-Saxon — and it has its critics. But it is justified in so far as it makes communication clearer. Unfortunately today one may be more familiar with unjustified over-complex language which the ignorant think is a sign of education. “Prior to” instead of “before” comes to mind.

Other advantages of the gerund

Often using a gerund allows one to drop an article and a preposition.

Often the use of a gerund allows one to drop an article and a preposition.

But an infinitive or active verb may often be better

The three successive prepositions in the sentence seem to me somewhat clumsy. Unless you have to stress the concept by placing it at the beginning of the sentence, the following seem to me better:

It is shameful of the Government to demonize people on benefits.

The Government should not demonize people on benefits. It is shameful.

*And I agree with @Heather about how there can be a difference in some cases.

These have a very slight but meaningful difference. Sometimes they are, indeed, interchangeable. But “the demonization” refers specifically to the state of have been demonized. Meaning, the state of the people. However, “the demonizing” refers to the action taken against them. The difference is extremely subtle, but one or the other may more accurately emphasize the main point or idea. Is the goal of the sentence to persuade your audience to have ill feelings about the government’s actions? Or is it to inspire sympathy concerning the state of the people?

In every day usage this choice probably would not merit so much consideration, and using either word would likely convey the message sufficiently. Either word choice is a correct use of language, but both words do have distinct meanings.