Google doesn't have a search API (it was long ago deprecated https://developers.google.com/web-search/). So the API itself is the advantage over Google in this case.
Did you read the link you provided? They actually mentioned right at the top that they have a newer search API which is recommended (though I'll admit that I missed it too at first).
Yes, I did :). As mentioned below, it's not a comparable product. Custom Search is site-specific. It's an API for the "search this page using Google" forms you sometimes see on blogs and the like. It's not an API for "capital S" Google Search, while Bing's API really is their Search API.
Ahh, gotcha. I thought Custom Search was that old thing they had which let you create a "customised" Google Search which had your colour scheme of choice and optional restriction of the results by topic (i.e. basically standard search), not the equivalent of 'site:x'.
the "custom search API" does not deserve the "search" in it's name. it's a different index, it's crap, and you can't access it as a whole, but only whitelisted parts.... google does not have a search API, it has a sad excuse to a search API
https://developers.google.com/custom-search/v1/overview