First off the biggest difference has to be acknowledged.
Blues have a salary cap.
Blues are exempt from claims they could have spent more because there is a hard limit, and they spend to it.
No matter what Cardinals spend, there can always be a criticism they could have spent more, because they could have. So it goes in salary-cap-less league. (A better criticism of the Cardinals, especially lately, is not what they spent but how they spent it.)
Armstrong has made a point to steer away from some of the legacy-type moves the Cardinals have made. David Backes and Alex Pietrangelo being recent example. Ryan Reaves to some degree.
Compare that to, say, the Carpenter extension and the reason behind it, the reason being the Cards said they didn't want to see Carpenter leave.
As for the trusting of internal options, both teams do that. That's probably their biggest similarity. What the Blues are poised to do with their young forwards -- Thomas, Kyrou and Koston -- is actually quite similar to what the Cardinals just did with their outfield. Hope offense comes from within.