First, both shows are simply fun. NCIS is a Bellisario show--Bellisario also created Quantum Leap. To sum up: Bellisario produces good, non-frills story-telling television.
Stargate is good story-telling television too. I don't consider the seasons after 4 as interesting as earlier seasons (although there are occasional great episodes). Nevertheless, both NCIS and Stargate provide non-pompous, unself-conscious, self-amused, and enormously relaxing television viewing.
I don't know if there is any overlap amongst the NCIS and Stargate writers, but the life/earth-saving teams of NCIS and Stargate have similar leads. As Eugene points out in response to my post about Stargate SG-1, both Richard Dean Anderson and Mark Harmon play leaders who verge on the edge of exasperation (although Mark Harmon's Gibbs is more tightly strung than Anderson's Jack).
And both Jack and Gibbs have a back-up or foil--Daniel (Michael Shanks) in Stargate and Dinozzo (Michael Weatherly) in NCIS. And despite their very different personalities, Daniel and Dinozzo relate to their respective bosses in similar ways.
(1) Both Daniel and Dinozzo are outsiders to the military. Daniel is an archaeologist. Dinozzo was a cop; in season 2, Dinozzo comments that Gibbs met him when he was a cop, giving the impression that Gibbs deliberately recruited Dinozzo.
By choosing outsiders as their "side-kicks," Jack and Gibbs show they are more flexible than other members of the military. This is effective character development, since both Jack and Gibbs (the heroes) must be relatable to the possibly non-military audience. Daniel and Dinozzo become the conduits through which viewers get to know the heroes.
In their side-kick capacities, Daniel and Dinozzo act as opposites to Jack and Gibbs. Daniel is more intellectual than Jack (not more intelligent, just more intellectual). Jack basically wants to fish, occasionally save the day (whilst thrashing the bad guys), and keep his team members safe. Daniel wants to read big books, translate stuff, look at old monuments, and read more big books.
Likewise, Dinozzo--possibly the most extroverted character on television--is "day" to his introverted boss's "night." Dinozzo is into technology, making him the antithesis of both Jack and Gibbs (Gibbs is especially grumpy about technology). He also makes most of the popular culture references on the show (in one of my favorite scenes in all NCIS, he tries to explain the symbol of the key in Millennium Actress to McGee).
By encapsulating the opposite qualities to their bosses, Daniel and Dinozzo enhance their bosses' positive qualities. Jack does not have to be the intellectual and fishing and arty and life-saving hero; he can be himself. (One of the best lines from season 7 is when Jack's "ghost" tells Carter, "Face it, Carter, I'm not that complex.")
Likewise, by giving Dinozzo all the "hip," up-to-date, cool jargon and toys, Gibbs remains the pure (ungadgety) tough guy. Since Weatherly is perfectly willing to play the clown, Gibbs can be grumpy about "cool" things but still look cool in comparison to Dinozzo (but the cool stuff is still there, even if Gibbs isn't the holder of the cool stuff).
In other words, the sidekicks for both Jack and Gibbs highlight their bosses' strong points while taking over or taking care of their weak points.
(2) On a girly note, Shanks and Weatherly are just soooo handsome and in the same way (although they actually look nothing alike): regular features with fairly strong jaw lines. That is, they are handsome without being pretty and much more relaxing to watch than pretty men. A pretty man, like a pretty woman, can startle and impress the viewer; beauty is its own reward (and has value). But it is rather like viewing too many impressionist paintings. Eventually, you want some meat.
For example, I've always found Gary Dourdan, David Duchovny and Chris Noth much more interesting to watch than Brad Pitt. Of course, sexiness matters as well--which Dourdan, Duchovny and Noth have in the extreme (Duchovny is one of those interesting actors where you get the impression, from the episode commentators, that his physical presence is actually even more charismatic than he comes across on the screen). Shanks and Weatherly are more damped down sexiness-wise than Dourdan, etc., but they have enough sexy vibes to hold your interest. Poor David James Elliott from JAG was, in my opinion, an exceptionally handsome man with about as much sex appeal as a toaster.
(3) Both Daniel and Dinozzo are funny. The only flaw in the Daniel/Jack exchanges is that both actors play the straight man (with Teal'c as the super-duper straight man). Still, Anderson and Shanks have good comedic timing, and Shanks can do the blank-that-was-odd look very well (although in Season 5, you can tell Shanks is bored out of his mind since that kind of look is all he does).
Dinozzo is the Costello of the Gibbs-Dinozzo relationship. He does good physical comedy; the season 2 opening credits show a hilarious clip from season 1 with Dinozzo "dancing." I admit when I first started watching NCIS, I was put off by Dinozzo's superficial sexism (more of this later), but either age has mellowed me or I perceive Dinozzo's character differently than I used to. I now consider him one of the funniest of the NCIS characters (although I have a soft spot for Ducky's conversation).
(4) Lastly, Daniel and Dinozzo both operate as moral centers of their teams. In Red Dwarf, Lister performs a similar function despite the fact that Lister is a slob and much less self-disciplined than Rimmer. Lister is more aware of the moral/ethical problems of a situation even if he doesn't stir himself to deal with them.
Likewise, Daniel operates as the ethical voice of SG-1. This doesn't mean the other members aren't ethical. It just means that Daniel performs that particular role. In the fascinating episode "The Other Side", Daniel continually objects to the lack of background information the team has collected regarding a group of potential allies. Exasperated, Jack tells him to shut up. Jack then has an unsettling conversation with the group leader at which point he apologizes to Daniel and tells him to continue collecting information. (And SG-1 learns that their so-called allies are basically Nazis.)
Jack immediately recognizes (possibly faster than Daniel) that the conversation is "off," and he immediately takes action. His ethics are just fine, thank you very much. But he also recognizes that Daniel's willingness to be the outsider, to look at multiple facets of an issue, provides a necessary counterpoint to the team's objectives. (I like it that Carter sometimes sides with Daniel and sometimes with Jack--unlike so many sitcoms, Carter is NOT the feminine voice of reason and goodness--none of that "If only women ran the world, life would be perfect" crap; I sometimes think the Stargate writers are the most non-sexist, commonsensical people in the world.)
Speaking of sexism, I think Dinozzo deliberately "acts" the part, mostly to annoy Kate (the character, not Kate, the blog writer)--that is, Weatherly is an actor playing the part of a guy who is partially playing a part. Dinozzo is far more reliable and down-to-earth than he comes across.
This shows up in his relationship with Gibbs. One of the most important aspects of the Dinozzo-Gibbs relationship is that no matter how often Gibbs rides Dinozzo, Dinozzo receives the hardest assignments involving the greatest degree of personal trust. Yet nobody ever comments on this fact. It's all so . . . manly and stiff-upper-lippish although Dinozzo's attitude is much more Dennis Quaid from The Right Stuff than Darcy from Pride & Prejudice. As Tom Wolfe writes in The Right Stuff, the astronauts will talk about flying, maneuvers, crashes, anything but the actual courage that makes them take the risks. This is Dinozzo. More than Gibbs, he is the guy who can walk away from the job. Similarly, he is the guy who can relax and find a joke in the most unpleasant of situations. His detachment gives him a degree of sanity that the other, more intense characters, lack. (But his basic loyalty is never called into question.)
I happen to love the Jack-Daniel/Gibbs-Dinozzo combination. I am not interested in the yaoi aspects of male bonding; rather I enjoy the good old-fashioned "we few, we happy few" band-of-brothers quality. Television and movies are beginning to show this type of bonding more between men and women, but it still remains, to a degree, the province of men. It's enchanting.