It's the first time this sort of thing has happened to my knowledge under the Disney-Ghibli deal, and I have no idea why, or whether they even use the same adaptive script. Either way, I have not seen the U.K. dub, so this is strictly a review of the U.S. version.
Directing/Script: Pixar veteran and award-winning sound designer Gary Rydstrom directed this dub, while Karey Kirkpatrick (Chicken Run, Over the Hedge, the U.S. Hitchhiker's Guide to the Galaxy film) handles the adapted script. They make for a pretty good team, although Kirkpatrick's script changes the names of Sho and Sadako to "Shawn" and "Jessica" for some reason. Considering that Ghibli supervises these dubs, I'm sure they agreed to it, and it certainly doesn't hurt the film. The voiceover at the end (much like the added positive lines at the endings of Kiki's and Spirited Away) is also apparently not in the Japanese version.
The one annoying thing about the dub is the shoehorned in pop songs. There *is* a vocal song that plays throughout the film during key scenes that is quite nice (and is presumably a dubbed version of its Japanese equivalent like in Laputa or Mononoke), but the quiet opening of the film has a generic tween pop number over it. It doesn't destroy the mood, but it does slightly hamper it. The other pop song, much like in Ponyo, plays over the end credits after a reprise of the main vocal song. It is equally generic and poppy.
ARRIETTY (Bridgit Mendler)-I seem to be noticing a pattern with the recent Disney dubs: they cast some of their latest brood of child/teen actors, I grumble about it, and then am pleasantly surprised by the high quality of their performances. This happened in Ponyo with the Cyrus and Jonas siblings, and it happens here too. Bridgit really is quite good in the role; she's the right age, she brings an appropriate amount of feisty energy, and she does a nice job with Arrietty's sadder moments as well.
SHAWN (David Henrie)-Shawn is a rather morose young man with a heart condition that he believes might kill him, but his attitude improves after meeting and helping Arrietty throughout the film. Henrie is perhaps a little quiet and deadpan, but that fits the role, and he does grow more energetic at times when it's necessary. No complaints.
POD (Will Arnett)-A friend of mine on another forum noted that Arnett's work here is "deceptively simple", and I would agree. Arnett actually has a good deal of experience in voice-over, having had roles in films such as Horton Hears A Who, Despicable Me, Ratatouille, Monsters Vs. Aliens, and video games like Eat Lead: The Return of Matt Hazard. This is probably his best role, though, and that's because he plays it note-perfectly. Pod is a calm, measured character who never speaks more than he has to, but he dearly loves his wife and daughter, and that all comes through in Arnett's work.
HOMILY (Amy Poehler)-Fun fact for you: Arnett and Poehler are married in real life! That adds an interesting subtext to Poehler's performance, which is my favorite in the dub aside from Arnett's. Poehler also has VA experience, most notably on Nickelodeon's "The Mighty B!", which she also created. She's a lot of fun here as Arrietty's frazzled mother, attacking the role with comic gusto, but also managing to be rather sweet and endearing in the process. I especially love her deliveries on lines like "Please promise me you won't let our daughter get eaten, or squashed like a bug" or when she ponders why she always thinks Pod has been eaten by the cat when he turns up late.
HARA (Carol Burnett)-The slightly nutty housekeeper, Hara serves as something of an antagonist in the film, but the curious thing is that she's not really that hateful. She's more of a comic force than an evil one, and Burnett is clearly having a lot of fun in the role. It's a little over-the-top at times, but that fits Hara's character, so she ends up as a real highlight of the dub as well.
Gracie Poletti and Moises Arias (Rico from "Hannah Montana") do a fine job in their respective small roles as Shawn's aunt Jessica and Spiller, a Borrower from another family who ends up serving as crucial help for Arrietty later in the film.
On the whole, this probably won't be one of my favorite Ghibli dubs, but it is a very good one nonetheless. I would definitely recommend checking it and the film itself out.