Where I think there is a difference is that the positional profiles for the Cowboys under McCarthy aren't as specific as they were under Garrett. This is where the whole "draft talented players, and we'll coach them..." comes from. Under Garrett, he had specific positional prototypes that he had the scouting staff go find. That in itself will reduce the number of players considered when building the draft board. For example, when Kris Richard got here, he didn't want a cornerback under 6 feet tall and with less than 32" arms. McCarthy isn't as restrictive.
You can argue that having a larger pool for consideration allows you more leeway in being able to select players, but at some point, the pieces have to fit together. This is where coaching comes in.