Offering a more serious approach to Ace Attorney's courtroom battles, The Great Ace Attorney Chronicles still offers a host of colourful characters and unlikely methodologies, but comes across as a very different game overall, for both good and bad. Thanks to Ace Attorney's brilliant localisation, The Great Ace Attorney's setup feels like a joke you have to explain to people: your protagonist Ryunosuke Naruhodo is supposed to be an ancestor of Phoenix Wright, who's originally named Ryuichi Naruhodo. The rename exemplifies a problem that up until very recently wasn't uncommon for Japanese media; the belief that a Japanese work's cultural connotations could confuse or overwhelm western audiences unless adopted as something else. It's a reason that's been used for not localising certain Shin Megami Tensei or Yakuza games, too.
The localisation made Ace Attorney in the west its own cultural product, amping up the silliness with punny names and references to western culture, but The Great Ace Attorney is a decidedly Japanese duology (some characters have still been renamed for that extra bit of punny goodness). It's set in the Japanese Meiji period, or the British Victorian era, a time of pivotal importance to both countries, and I see both games as comment on that time in history, rather than a collection of increasingly dramatic court cases.
Circumstances of the first case thrust the hapless Ryunosuke into the limelight, suddenly required to defend himself in court. You learn all the mechanics of previous Ace Attorney games - you listen to witness testimonies, followed by a cross-examination. During the cross-examination, you can ask witnesses to elaborate on a statement by pressing them on it, potentially gleaning new information in the process. Your court record holds all your current evidence, and once you spot a statement that's inconsistent with the evidence, you present it with the famous shout of "Objection!"