Are these compatible bottom brackets?
Matching BB is one of the hardest jobs as a paper exercise compared to eyeballing them side by side.  As suggest in @Batman comment, length and offset are both critical, yet most sellers only specify length. 

As far as matching Cranks go, there are a  number of systems - square taper was (an probably still is) the most common - there is some confusion over the compatibility between a couple of different standards, but it does not seem to be a problem in reality. Spline cranks come in a couple of different flavors, which are incompatible. Have a read of Sheldons webpage on the subject.