It's a good question. I would generally say that they are semantically pretty equivalent. I would also agree that I might be more likely to say "the murder of a man" than "the use of a stolen credit card" in this context, but not for grammatical reasons.

The primary difference to me is rhetorical: "the murder" has some gravitas and the sentence is interesting even without the extra bit of information about it being the murder of a man, etc. However, "the use" is not interesting — it's the "stolen" part that's interesting. So, there is no benefit, from a stylistic point of view, to calling out "use." Contrast this with the following more likely news item:

"Police arrested a man for the theft of multiple vehicles in the area." (Sounds good to me.)

"Theft" is a more interesting noun than "use", so that might be why this works to my ears. It's difficult to construct the same news item with stolen credit cards, because the primary offense is not really stealing the credit cards ("the theft of credit cards" does not really sound like much of a crime), but rather buying items with that stolen credit card.

From that intuition, I would conclude that using "the murder" construct (versus the "murdering …" construct) puts extra attention on the act, whereas the gerund (-ing) construct is neutral in that regard.

Naturally, you get fewer hits for stealing a credit card: the police rarely arrest people for such a trivial offence, and if they do, it's even less likely reported in the media. Murder, on the other hand...

It's risky trying to do any statistical analysis on small numbers: for example, the results can easily be disturbed by just one quote about one incident, if the quote is reported multiple times in different publications.

To answer your question: for formal publications like statements issued by the police, I don't think that there is any significant difference in preference of gerund vs the-noun-of. For informal speech, probably the gerund has the edge.