I feel like none of the other games' stories can stand on their own like the first game's can. The rest of the trilogy are direct sequels which don't make much sense without it. Of course, that isn't a flaw in itself, it just means that their stories don't mean anything without the original, making the three effectively one big story.
In AA, the cases progressed linearly, and each one had a place in the story. 1-1 introduced Phoenix, Larry, Mia and the Judge. The next two had important story developments(Mia's death, Edgeworth helping Phoenix).1-4 was the finale which connected many characters and story elements from every case and had a proper ending. It was also incredibly funny and a satire of the Japanese court system.
JFA begins as an amnesia story, but not only does it drop that immediately (That's not necessarily a bad thing, but letting it continue throught the game could have made for interesting developments - of course, it would have destroyed the point of ther story: JFA is about what it means for Phoenix to be a lawyer.), it even has the second case take place before the first one. Knowing that Maya is alive and well and not in prison in 2-1 negates any tension in 2-2. JFA has no overarching story - instead, its cases are connected tematically. Overall, I think that makes it weaker.
T&T does non-linear storytelling much better than JFA. It mixes Mia's cases with Phoenix's in such a way that the aforementioned problem doesn't exist. There is an overarching story, but it takes a back seat in 2-2 and 2-3. 2-2 exists to introduce Godot, 2-3 exists because going from 2-2 to 2-4 would make him much less mysterious. Also, there was a hint for the last case(ketchup) in 2-3, which is pretty cool. The third game definitely has a good story, though returning characters and plot elements make it not standalone, but part of the trilogy.
The trilogy's story, when taken as a whole, seems a little unfocused at times, but is internally consistent(mostly), and complete.
Then there's AJ. The trilogy clearly didn't need a continuation, and the change in main characters really made for interesting mysteries, and on the surface, it seems to make the story capable of standing on its own. There was so much potential in telling a story about Phoenix falling from grace, after having become a legend. Sadly, some of the decisions made for the story make it much, much weaker than AA's.
AAI is an interesting case. It's not a direct sequel to any of the previous games, but it suffers from similar problems. For example, all the cameos may be for fanservice, but are detrimential to the story IMO. Non-linear storytelling is used here like in JFA, but the problem about the tension is intensified even more. The first case takes place before the last one, but after the other three, making the last case the only one to really have dramatic stakes. Also, the overarching story is not really that engaging, because while it seems to be about Edgeworth tracking down a smuggling ring, Edgeworth only solves some murders that involve people affiliated with the smuggling ring. Taking down the smuggling ring just seems like a side effect of that. While the game builds up another plotline(Yatagarasu), the finale is not about that. It gets resolved before the main plot. Overall AAI is very impersonal, which is another reason why I think it's a weak story.
Now, AAI2 is much better. The cases are presented in a linear order (with a flashback within one case), eliminating the tension problem. The story builds not only on its predecessor, but also expands on things PWAA left unexplained(because they were not important). That does mean that it can't stand on its own, but makes it a good sequel to AAI, and provides fanservice without pandering to nostalgia(at least not with the main story). But the thing that really makes AAI2 the best story since the trilogy is that the cases not only follow each other closely(meaning that the game takes place over a very short time compared to main series games), but they are so interconnected that they don't feel like they just happened to occur after each other, like in AAI, but are actually part of one cohesive narrative. This cohesive narrative is what makes the story compelling.
After having played AAI2, I'm quite baffled by DD. It's a step backwards in terms of story, and frankly, it's kind of a mess. I think it's the worst offender when it comes to using non-linearity. 5-1 takes place in the middle of 5-4, making the two cases inbetween tension-free. Especially 5-3, which has the same defendant as 5-1! And since 5-4 and 5-5 are basically the same case anyway, there's hardly any tension in the game at all. The narrative is anything but cohesive, especially with the three protagonists. None of them get even two full cases! (Not counting the DLC case, which is not part of the main story anyway.) None of them get any meaning ful development. Actually, no main character gets any meaningful development. The game really doesn't have an overarching story, just new characters who meet up in the last case in which Phoenix solves the mystery in ther past and present.
DD also suffers from "plagiarism", which is what I call taking elements of old cases and putting them in a new context, basically pandering to nostalgia on a story level, which just comes off as lazy and/or uncreative. Yes, the previous games reused elements of old cases, but never this many. Also, they made the hints WAY TOO OBVIOUS, especially for big reveals. This made the game too easy, which made it less fun.
Another obvious problem is the lack of continuity starting from DD. None of the unresolved issues in AJ were really addressed. Not only that, 5-5's ending raised so many questions that were never answered in the next game.
SoJ was better. There's no problem with non-linearity this time, and it's not as blatant with the hints - at least most of the time. I actually really liked the premise: Phoenix comes to a country which is about to have a revolution. This could have allowed it the freedom to become a great standalone story, maybe even incorporating some satire, which has been missing from the series for a long time. Sadly, the execution let me down. 6-2 and 6-4 had nothing to do with the story, they could have been cut in their entirety without losing anything. 6-1 and 6-3 were decent cases, I guess. 6-5 was interesting in that it was really two cases in one. I liked the first one(except for the whole thing with Phoenix, that was a horrible decision). The second part wasn't horrible, but I felt like the way they handled the "revolution" just left it as wasted potential. Overall, it was better, but not a great story, and it definitely doesn't stand alone in any way. (And it still has the "plagiarism" problem. And retcons.)
So, to sum up: The series has had its ups and downs, sure, but the last two games worry me because they are setting a dangerous precedent. If they keep expanding the series DD/SoJ-style, it will never go anywhere. Introducing more lawyers, "powers", prosecutors, plotlines that go unresolved in the last cases and are never brought up again, reusing old elements will just make Ace Attorney a disjointed mess with no overarching story, no focus, no direction.
I just hope GS7 will be better.