Can "equivalent" and "counterpart" be interchangeable in the context below?

Solution 1:

No, they aren't interchangeable here. Neither of them work. Equivalent is an error and counterpart is being used in a nonidiomatic way, although the general sense of the word is appropriate to the sentence's objective. BoldBen's answer handles the counterpart issue.

Equivalent is used when establishing a comparison, not when establishing a contrast. So you can say

The test scores had different distributions—a score of 80 on test A being equivalent to an 83 on test B.

Here you are establishing differently-valued numbers as equivalent statistics.

Equivalence is about establishing interchangeability between easily distinguishable things. 1/2 and 2/4 are equivalent fractions. It doesn't work with contrasts because contrasting items are not interchangeable.

In a related question Equal vs equivalent ..., John Lawler wrote in a comment

... whereas equivalent means 'is a satisfactory substitute for'. And substitution requires a context.

Clearly, in the example statement, satisfactory substitute for is not the context.