DR first is used by most of the world-level rouxers today including Kian Mansour and Sean Villanueva. Most of the existing SB resources are built on top of it. It is easy to make progress with, as it greatly simplifies tracking and pattern recognition for SB blockbuilding.
Freestyle, in contrast, allows you to be flexible with how you build the second square. It is a superset of DR first. Strategies include make a pair then insert the remaining edge, or insert any edge then insert the remaining pair.
The consensus is while freestyle potentially leads to better efficiency, it is more demanding of your recognition and tracking skills1. Empirically, it has yet to be proven that freestyle can serve as a standalone strategy to attain a speed level comparable to those using DR-first.
In general, DR first is recommended to beginners and advanced cubers alike as the dominant strategy, while freestyle can act as a supplement, offering shortcuts to building SS whenever you happen to recognize a few easy freestyle patterns as they show up. These SS techniques will be mentioned in the section below.
Gilles Roux's website [insert link] features some of these algorithms.
1: (Most SS strategies are such that once you solve the starting piece/pieces the SS becomes fixed meaning you're left with no options or freedom to select in what order to continue to block-build, whereas DR-first is the only exception among these strategies to NOT fix the SS but rather enables you to choose any of the two remaining pairs (SP). The very existence of two competing options alone would boost the chance of there being a good case, and additionally create room for influencing techniques. Therefore, in order to beat DR first on average, you would need more information about SS, e.g you saw DR is bad and another edge is good and the corresponding SS corner can be paired in such a way that gives an easy SS finish, etc. )