The best illustration of why it's important can be seen by comparing several series.
In her Pern stories, Anne McCaffrey generally keeps published order and chronological order similar. There are exceptions, most notably Harper Hall trillogy parallels the second two books of the Dragonriders Trillogy, and Moreta and Nerilka predate both, and parallel each other.
Neither Moreta nor Nerilka are that engaging on their own; knowing the related events by the teaching ballad excerpts in the earlier published works increases both enthusiasm for them and the issues of inherited personality traits (without mentioning whether they are genetic or environmental, tho' Jaxom seems to indicate the author believes a mixture of both).
In this case, reading in publication order is superior, tho' either trillogy is a fine start point; Dragonriders second already has spoilers galore in Harper Hall, but if one reads Dragonflight and then Harper Hall, they are minimized. Moreta and Nerilka answer questions which arise only from reading the Dragonriders and Harper Hall trillogies. Later works include multiple time frames in the same volume, and build upon prior works in both timeline chunks, but again, publication order is essentially chronological order for each of the 3 major timeframes.
In the case of Bujold's Vorkosigan series, I have read them in both publication order and chronological order. With the exception of Cetaganda, they work best in a unique order:
The Warriors Apprentice OR the omnibus Cordelia's Honor as start point. Then the other. Then chronological following of miles. Then the distant prequel, Falling Free, followed by Ethan of Athos, as, like Moreta and Nerilka, they answer questions raised in the main, but unlike those two, either can stand alone viably. Cetaganda suffers slightly for this, but it is an excellent book in its own right.
Captain VorPatril's Alliance and
Gentleman Jole and the Red Queen are novels that seem to stand alone; Gentleman is strongly tied to many items; it benefits even from following the side novels. It's truly a "capstone" work - supported by all which were published prior. Alliance is strongly tied to prior novels as well, but can stand alone.
Both Alliance and Gentleman Jole include major spoilers, if read out of chronology; both are the latest two in writing order, release order, and chronological order, however, so it's not much an issue.
In the Dune sequence, most of the Brian Herbert & Kevin J. Anderson "House" series of prequels add consistent depth to many characters from the main Frank Herber Dune-Chapterhouse sequence. While they could be read prior (and my purchase of them lead to rereading the Dune-Chapterhouse sequence), they are far more interesting when one sees how BH/KJA work FH's notes into a viable prequel. They reveal new information, but also just how small the actual courts of the Imperium are. The stories are often considered non-canonical by some fans, but are firmly based in FH's notes, and the relationships revealed are consistent with canon. They should not be read before Dune, and probably not before Messiah and Children, but can be read at any point after these without too many spoilers.
The main sequence (Dune, Messiah, Children, God-Emperor, Heretics, Chapterhouse) could be followed easily by Hunters and Sandworms, ignoring the prequels entirely, and not miss much at all, but certain characters will be "new" in that case. (I'll note that, when I hit the ending of Sandworms, I had to check a bunch of stuff in the main sequence to confirm it, but the ending was very much a "DUH!" moment for me.)
The distant prequels are an excellent story, but feel decidedly off. The only reasonable place to read them is before hunters; Hunters and Sandworms both spoil certain elements of the series. While I had read them prior to Hunters and Sandworms, I'd not read them in some time, and the links to them were not terribly obvious save for the names of certain characters. That said, they do stand alone fairly well, and could be read on their own prior to any of the others.
Some of the newer prequels fall into the "Shouldn't be read" category; Paul of Dune was decidedly not in line with what I expected... and unfinishable for me. Worse, it's a timeline jump novel... it starts in one timeline, then changes to a different, earlier one.
The non-canonical book, Road to Dune, includes an early draft of Dune and explanatory essays on the main sequence. The early draft can safely be read after Dune, but the essays should not be read until the main sequence has been.
The original main sequence (Ender's Game, Speaker for the Dead, Xenocide) are a cohesive unit, with some large gaps. The parallel Shadow sequence (Ender's Shadow, Shadow of the Hegemon, Shadow Puppets and Shadow of the Giant). takes place from the same time as Ender's Game to just prior to Xenocide.
Both sequences have minor spoilers to the other when read in chronological order.
First Meetings is a collection of short stories; on their faces, they are not great stories themselves, but they answer questions raised in the main sequence and Shadow sequence.
According to the Wikipedia entry, Card suggests that children of the mind be read immediately after Xenocide, but otherwise apparently expresses no preference. I recall having read that advice from Card, as well.
Since each novel has both an internal arch, and is part of an external arch involving the particular sequence, threaded is probably best. Pick one thread, read it through in chronological order, then the other, then the subsidiary works.
Wikipedia's Ender's Game Entry has a map showing the two main threads and the timeline ordering.
Which order, publication, chronological, threaded, or other, varies by series.