Other way around. Europe started HBP started first, then US announced the BI. The HBP is centered around Markham's big sim project. The BI is more like a bag of somewhat related grants, focusing more on connectome mapping. From what I remember, both projects are long term, and most of the results are expected to be 5 years out or so, but they are publishing along the way.
https://www.whitehouse.gov/blog/2016/05/03/preparing-future-artificial-intelligence