Third-person: Didactic, Moralizing, Poetic; First-person: Matter-of-Fact, Reportage
In most of his novels, Dickens uses a few repeated tricks and touches. Because his style is so easily identifiable, he's the kind of writer that's called a "stylist" – meaning that the style of his prose is really important to him and he enjoys playing with language in a way that many otherwise talented writers do not.
In Bleak House, this playful and often poetic style is used only for the third-person narrator. To create contrast, Esther's voice is straightforward and normal, without the crazy flights of verbal fancy that are the Dickensian trademark. A good way to see the differences is to compare the two narrators describing the same thing. Let's go with the Jarndyce court case, shall we?
Here's how the third-person narrator sees it:
Jarndyce and Jarndyce drones on. This scarecrow of a suit has, in course of time, become so complicated that no man alive knows what it means. The parties to it understand it least, but it has been observed that no two Chancery lawyers can talk about it for five minutes without coming to a total disagreement as to all the premises. Innumerable children have been born into the cause; innumerable young people have married into it; innumerable old people have died out of it. Scores of persons have deliriously found themselves made parties in Jarndyce and Jarndyce without knowing how or why; whole families have inherited legendary hatreds with the suit. [...] Jarndyce and Jarndyce has passed into a joke. That is the only good that has ever come of it. It has been death to many, but it is a joke in the profession. [...] The last Lord Chancellor handled it neatly, when, correcting Mr. Blowers, the eminent silk gown who said that such a thing might happen when the sky rained potatoes, he observed, "or when we get through Jarndyce and Jarndyce, Mr. Blowers"--a pleasantry that particularly tickled the maces, bags, and purses. [...] How many people out of the suit Jarndyce and Jarndyce has stretched forth its unwholesome hand to spoil and corrupt would be a very wide question. From the master upon whose impaling files reams of dusty warrants in Jarndyce and Jarndyce have grimly writhed into many shapes, down to the copying-clerk in the Six Clerks' Office who has copied his tens of thousands of Chancery folio-pages under that eternal heading, no man's nature has been made better by it. (1.7-10)
Here we see all the stylistic tricks Dickens typically has up his sleeve. There's the repetition of key words and phrases (a technique called "anaphora." Use this in your next English paper for an instant grade bump!): "innumerable children"/"innumerable young people"/"innumerable old people." There is the making of long lists: maces, bags, purses (all jokey references to the various kinds of lawyers involved). There are the self-defining names: the eminent Mr. Blowers is clearly a guy who blows a lot of hot air. And of course, let's not forget the hyperbole (exaggeration): the number of people involved with the suit is not just large, but actually uncountable; the lawsuit creates not just hostility, but epic feuds between families.
What is the point of all of these tactics? Maybe it's a way to give the Jarndyce lawsuit a kind of magical, ominous, world-defining quality – to take it out of reality and put it in some kind of mythical realm.
Meanwhile, here is Esther talking about the same thing:
When we came to Westminster Hall we found that the day's business was begun. Worse than that, we found such an unusual crowd in the Court of Chancery that it was full to the door, and we could neither see nor hear what was passing within. It appeared to be something droll, for occasionally there was a laugh and a cry of "Silence!" It appeared to be something interesting, for every one was pushing and striving to get nearer. It appeared to be something that made the professional gentlemen very merry, for there were several young counsellors in wigs and whiskers on the outside of the crowd, and when one of them told the others about it, they put their hands in their pockets, and quite doubled themselves up with laughter, and went stamping about the pavement of the Hall. [...] The people came streaming out looking flushed and hot and bringing a quantity of bad air with them. [...] Presently great bundles of paper began to be carried out--bundles in bags, bundles too large to be got into any bags, immense masses of papers of all shapes and no shapes, which the bearers staggered under, and threw down for the time being, anyhow, on the Hall pavement, while they went back to bring out more. Even these clerks were laughing. We glanced at the papers, and seeing Jarndyce and Jarndyce everywhere, asked an official-looking person who was standing in the midst of them whether the cause was over. Yes, he said, it was all up with it at last, and burst out laughing too. (65.5-9)
Wow, talk about deflation. The details are much the same: people are laughing at the ridiculousness of this lawsuit, there's a whole bunch of paperwork associated with it, and it's hard to imagine that Jarndyce and Jarndyce might actually come to an end. But check out the difference in delivery: no repetition, no funny lists – it's "just the facts ma'am." Esther doesn't exaggerate anything she sees – she just tells it like it is, noting whatever details pop out at her.