SG1, for most of its run, hinges on a near constant dissection of moral philosophy as presented by opposing view points in a given situation. The dichotomy between Jack and Daniel is presented as the core of the show, in an episodic morality play which focuses on deep and resonant themes in the grand tradition of sci-fi shows like Star Trek and Doctor Who before it. In this way, SG1 can almost be treated as the prompt for a moral-of-the-week discussion course, as it was for many years in my household with my own children.
This took a back seat in the later seasons as the show took a more lighthearted and adventure-based tone, centered around its own expanding mythology. The addition of fun and loveable characters like Mitchell and Vala, came at the cost of the thematic opposition to Daniel's often debated perspective, which can be exemplified through the total lack of argument revolving around "whats the right choice" scenarios between Daniel and Mitchell.
Where Jack and the militaristic nature of the core SG mission often stood in stark contrast between duty/practicality and Daniel's persistent discussions of moral philosophy and spiritualism, this dynamic was lacking after the departure of RDA as a cast regular. Vala's personal journey and redemption instead filled this void in the final seasons, as the question of what is right in a given scenario was shifted toward the more general struggle to overcome one's own faults and seek a more selfless life.
Stargate Atlantis, while occasionally able to capture some essence of these themes -- specifically regarding the rock versus a hard place decisions faced by Weir in particular -- mostly chose from its outset to focus less on philosophy and more on popular entertainment. The distance from Earth and removal of legal restrictions regarding experimentation, torture, human rights etc, is brought into the forefront through several arcs, but ultimately any message is entirely lacking in conclusivity or conviction, as no character present through the series' entire run is written quite as effectively to such ends as Daniel Jackson was within SG1. There is no moral center, only an occasionally questioning uncertainty presented through Weir's leadership and depiction. The show is fun and adventurous with greatly likeable characters, action, set pieces etc... it just never captures the heart of its predecessor.
SGU was a marked departure in all regards, seemingly lacking any foundational character who had what I might call a moral center in the first place. It's darker, grittier, and deals in shades of human failings more often than aspirational virtues. Rather than focus on fun and adventure, it seems to relish instead the theoretical sciences of the franchise mythology, while basking in just how unlikable its central cast can be, while still being considered protagonists. It's primary audience surrogate Eli, is a passenger who holds little authority but perhaps more merit than all of the show's other characters combined, and yet he never truly comes into his own to fill the role of hero, as he rightly should have if the show were renewed further.
So... in summation,
SG1 was a philosophy class in a bottle each week, filled with exciting and entertaining characters all striving to live up to their most heroic and virtuous ideals.
SGA was a more cut-and-dry adventure-of-the-week, which occasionally dipped its toe into questions of moral ethics.
And Stargate Universe was an exercise in sci-fi nihilism.