"'To'/'on' the contrary" in these sentences: is the difference very slight?

Solution 1:

"To the contrary" is a directional phrase, and will need to be used as a predicate, or subordinately to a predicate. This is why the first instance says "Now it is to the contrary" This form is to be equated with something IN the sentence itself.

"On the contrary" is a locative, and is to be used more logically in a sentence. As an interjection. Thus the second example has a comma following, it is an interjection. Also it is why the dictionary definition says that it is "used to intensify..." This form is to be equated with the statement as a whole.

Solution 2:

The ODE definitions that you cite confirm my instinct, that the two NYT excerpts are both correct. I wouldn't use these two expressions interchangeably, although the meanings are certainly similar.

Since (by the ODE definition) "on the contrary" just intensifies a statement, it would be incorrect in the first sentence. You wouldn't say "Now it is and what we are seeing is a slow evaporation of the parking spaces", so you also shouldn't say "Now it is on the contrary, and what we are seeing is a slow evaporation of the parking spaces".

However, in the second case, you could say "The spirit of Senator Simmons's article is not very humane or broad; it is rather narrow and harsh." Adding "on the contrary" just intensifies the contrast, rather than introducing a new idea, so it's the correct phrase to use here.