There are no strong differences between the two in literal meaning, but adaptability is used far more commonly than adaptiveness. I have done a few searches (one in Corpus of Contemporary American English, one in British National Corpus, one in NGram) to demonstrate the difference.
I ran a Compare search in COCA. These searches highlight which words are used frequently with one term but not the other. So they can provide clues as to what contexts words tend to be used, in addition to showing raw frequency of use.
The top 25 for adaptiveness mostly involve words related to organizations. In actuality, almost of the top results all come from the same article: Hamid, A. A. (2017). Strategic, structural supply chain orientation and operational adaptiveness. Journal of Business Studies Quarterly, 9(1), p. 52-64. So adaptiveness is a key term the author uses to define a specific phenomenon of study in Supply Chain Orientation (SCO), but it is not a commonly used word otherwise.
Adaptability has more varied results. It is hard for me to distinguish a pattern in the top results: flexibility, cohesion, family, change all seem like pretty common collocations I'd expect.
Just to make sure this isn't an American-specific thing, I also ran the same Compare search in the British National Corpus (BNC). Similar result: adaptiveness is seldom used, and mostly from one source with incomplete citation information: British Journal of Social Work, 1991. Adaptability is used much more widely; I only noticed written results rather than oral interviews.
NGram visualizes how infrequently adaptiveness is used in printed work.
Adaptability has long been the more common term.
The terms may be interchangeable in literal meaning, but adaptability is the more common word.