I have been impressed by how (relatively) distinct House's new team is from the old team. Relatively--they come off a bit flat in the middle of the season, but I put this down to the writers' strike. House seasons usually contain two arcs: the main arc at the beginning of the season followed by a bunch of loose episodes followed by a small arc at the end of the season. Season 4 skips straight from main arc to small arc. All the get-to-know-them-better episodes are missing which makes the distinctiveness of the new team doubly impressive.
Having said that, I think the new team members fulfill similar roles to the old team members: House needs certain types of people around him.
First, House needs someone who will disagree with him. As Dobson (played by the marvelous Carmen Argenziano--Carter's dad for you Stargate fans) points out, House doesn't need someone to tell him what he thinks. Rather, House needs the stimulus of a hard logical mind that comes at problems from a different perspective than his own. This is one reason House gets so annoyed with Foreman's "que sera sera" attitude in Season 2. House wants conflict because conflict enhances his ability to process a problem.
Setting aside the fact that both Cameron and Thirteen are beautiful women (and, as House discovers in the hilarious Ugly, he does prefer his female doctors to be pretty and smart), Cameron and Thirteen force House to consider psychological explanations as part of the diagnosis. Cameron is more of a people-person than Thirteen; Thirteen possesses a remoteness that Cameron would like to have but simply doesn't. Still, Thirteen, like Cameron, is apt to ponder "why" when it comes to a patient.
Basically, Thirteen and Cameron are Wilson, and House needs Wilson. House may loathe psychiatrists, he may mock Wilson's psychoanalyzing, but he wants the pressure to understand a patient's mindset, not just a patient's physical health. (One of the best indications of this is in Season 1, "Kids," when House realizes that Cameron would have learned about bathing-suit-girl's relationships long before Foreman, Chase, or House.)
Chase has always been one of my favorites. I think he adds a nice, occasionally deadpan, contrast to Foreman's ambition and Cameron's preoccupation with House. I could never understand, though, what led House to hire Chase in the first place (he was the first person hired of the old team).
Kutner's selection made Chase's selection clear. Both Chase and Kutner are odd men out: they have interests that lie beyond medicine--interests, in fact, that make them immune to good doctoring (and sometimes prone to bad doctoring, as when Chase misses a diagnosis while in emotional shock--an event House takes responsibility for). In Season 1, when Chase betrays House, he does it to save his job, not his reputation. Unlike Foreman and Cameron, he isn't a natural diagnostician, but he becomes a very good doctor under House's aegis and would probably make a fantastic GP. But, ultimately, the job doesn't run Chase. Once he falls in love with Cameron, for instance, he is perfectly willing to go where Cameron goes, not to the best position. This lack of ambition, oddly enough, gives him the capacity to walk away from House's games in Season 4 more than Foreman and Cameron.
Likewise, Kutner likes danger, blowing things up, magic, and secret Santas--non-medical things. Like Chase, he has a wryness that makes him more attune to House's humor. (Kutner also has a gentle guilelessness about him that makes him extremely appealing.)
I think House needs a Chase/Kutner for the same reason House needs clinic duty (no matter how much he resists it). Foreman/Taub may think differently than House. Cameron/Thirteen may go down roads he would prefer to ignore (but knows he can't). Nevertheless, for Foreman/Taub/Cameron/Thirteen and for House, medicine--the case, the patient, the solution--is the controlling interest. For Chase/Kutner, it isn't. House needs this. He needs not just his mirror-self but his non-self.
The result, at least between House and Chase, is a subtle sweetness that House really only shares with Wilson. Chase is the first person House "sees" in Season 4. When Chase shows up in surgery, the potential team members ask, "Are you going to hire him?" Instead of making one of his snarky replies, House glances up at Chase in the observation booth. Chase shakes his head, an almost imperceptible but distinct motion; then, House makes his snarky comment. He allows Chase to make the decision, rather than forcing his decision on Chase--not something he commonly does with Foreman or Cameron.
Not that Chase and House could be friends. Chase isn't Wilson. But there's a purely human, non-doctorly element to their relationship that is missing from House's other relationships. Time will only tell if he establishes the same rapport with Kutner.
I think House's team member choices explain, to an extent, why he is so much fun to watch. I've been surprised by how much I like Amber, House's other-self--even before she started dating Wilson! There was something refreshing, even amusing, about her complete ruthlessness, her desire to pursue her interests at all costs. House has this quality plus another that Amber, cut down in the prime of life, lacks: he wants to be stimulated, he wants to think outside the box, he wants to be shown a different mindset; he even, sometimes, wants to be wrong. He may be arrogant, obnoxious, condescending, and a thorough jerk, but his willingness to test himself, constantly, against different selves excuses many of those flaws.
And makes him devilishly fun to watch.