(wanted to mention; due to my, "habit," of pre-ordering all of the Japanese versions of the games in the series since 2012, I refer to the RGG series {and spinoffs} by their Japanese titles, just in case it's confusing!)
It is natural to compare the two; the majority that played 'mue first, then the RGG series, went into it like that. I kinda did, but I just loved the series from moment 1, that the lack of immersion didn't bother me at all and I completely forgot about 'mue once I got invested into the story
.
They did do fully-voiced (save for people on the street, with text bubbles) in RGG 6, but that's been the only game in the series to have it fully-voiced, thus far.
I find that the 5 games' (3 'mue, 2 Judge Eyes) are only somewhat similar in that you are investigating something, but even then, the approaches, settings, situations and subject matter, are completely-different and unrelated, thus they I find they aren't alike at all.
To use a comparison I like to qualify, think of the two series in terms of television shows; each RGG game starts off and then ends, tying up what it started with (Judge Eyes included), so each game is essentially a season of a TV show. 'mue on the other hand, is a LONG runner, where each game is just a part of a greater whole, like a soap opera or long-running serial, that isn't defined by seasons or a clear start and end.
To further break it down, I'll put it this way:
RGG series, if they were all running together:
MAIN:
Season 1: RGG
Season 2: RGG 2
Season 3: RGG 3
Season 4: RGG 4
Season 5: RGG 5
Season 6: RGG 0 (a flashback season)
Season 7: RGG 6
Season 8: RGG 7
SPINOFFS (note; these aren't the series' actual names; they have none, it's just a suggestion, to better group them)
:
"The Samurai Years;" Season 1: Kenzan!
"The Tatsuya Stories;" Season 1: Kurohyo: RGG Shinso
"The Tatsuya Stories;" Season 2: Kurohyo 2: RGG Ashura Hen
"The Samurai Years;" Season 2: Ishin!
"Judge Eyes;" Season 1: Judge Eyes
"Judge Eyes;" Season 2: Lost Judgement
MINI-SERIES (same thing with the names in quotes)
:
Mini-Series: "Zombie Outbreak:" RGG Of the End/Dead Souls
Mini-Series: "Post-Apoc Wasteland:" Hokuto ga Gotoku
So if you put all of the non-remake games together, you can have spinoff series and mini-series running at the same time (like Law and Order had or Saved by the Bell, etc.)
Main Series Season 1: RGG
Main Series Season 2: RGG 2
Spinoff Series: "The Samurai Years;" Season 1: Kenzan!
Main Series Season 3: RGG 3
Spinoff Series: "The Tatsuya Stories;" Season 1: Kurohyo: RGG Shinso
Main Series Season 4: RGG 4
Mini-Series: "Zombie Outbreak:" RGG Of the End/Dead Souls
Spinoff Series: "The Tatsuya Stories;" Season 2: Kurohyo 2: RGG Ashura Hen
Main Series Season 5: RGG 5
Spinoff Series: "The Samurai Years;" Season 2: Ishin!
Main Series Season 6: RGG 0 (a flashback season)
Main Series Season 7: RGG 6
Mini-Series: "Post-Apoc Wasteland:" Hokuto ga Gotoku
Spinoff Series: "Judge Eyes;" Season 1: Judge Eyes
Main Series Season 8: RGG 7
Spinoff Series: "Judge Eyes;" Season 2: Lost Judgement
Whereas for Shenmue, you have the GDC chapter cards and a base timeline and are guaranteed 11 or 16 or whatever seasons, with each season represented by amalgamations and gives and takes from the chapter cards (as 'mue II takes from cards 2 and 4, while 'mue III takes from cards 4, 5 and 6, etc.).
There is a defined beginning and end to the plot of each game in the RGG series, with little (if any) characters, situations or events spilling into multiple games (settings/locations however, are indeed represented in almost every subsequent title), while 'mue has a defined villain, defined settings and a long, slow, overarching plot that is incredibly-fluid, in the time it takes to traverse through it.
Sorry for the essay lol. The two franchises are my two favourite on the planet and 'mue II is my 3rd-favourite game of all-time, while RGG 3 is my 4th-favourite game of all-time. I love both franchises to pieces and have played each title in both franchises (save for LJ, Judge Eyes, RGG 7 and 'mue III), at least twice, so I can say with confidence that I have seen almost every little detail there is to see in each of the games above (and the games that aren't listed, like the Kiwamis).