"The only jazz standards book I own is the cliched Real Book 6th Edition Vol 1."
Why is this "chiched"?
Also, with a bounty on this question I think it should be less broad and more specific but that's just my opinion.
w/r to Real books and anthologies in general you will never get great arrangements. These books are meant to help working musicians get a quick peak at the basic structure of a tune. They are like cliff notes and you would not pass an exam (or at least do poorly) having read only cliff notes.
"I'm going to fix that soon by getting another book or three, but I'm not sure whether there are other comprehensive jazz chart anthologies that can stack up. Are there others worth picking up, including Real Book Vols 2 and 3 or any good online fake books? Or maybe other standards collections would be diminishing returns at this point, and I should focus on musician or style-specific books?"
This depends on what you are trying to achieve. If you want to really learn Jazz, or any style of music you need to immerse yourself in that music, and the culture of that music. You cannot really learn Jazz from the real book. For a guitarist this would amount to playing a constant barrage of Freddie straight 4 (ii-V7)'s in the circle of 5ths all day long. As dmb pointed out, there are "errors" in the Real Book, both in melodies and chords. Despite that I think the Real books are the best value for the money (but I got my first one in the late 70's early 80's when they were probably bootleg). They were a quarter of the price as a published Fake Book and i.m.o., and despite my previous comment, had descent changes. I own a "World's Greatest Fake Book" and it is anything but that! The printing quality is better than the Real Book, but they crammed 1000's of tunes into it, small font, and the chords are mostly Maj and Min, not a lot of extended chords. For a guitarist this doesn't give much to work with.
However, if your goal is to have a quick reference to a large library of tunes to pull out and play at a low key gig then any of these are great resources. Like I said Real Book has worked well for me but they are all similar in look a feel.
A better idea is to devote some time to the following, if you haven't already
Studying music theory and how chords move in a progression. Why? Because there really are only a few meaningful sets of changes and you start to see why when you study music theory. After some time the movement of the chords makes sense in a way that transcends a particular piece. The melody hints at what chords to play and you start to rely less on the handicap of the charts and just follow your ear. When you can do this then you really can be creative with a simple cheat sheet. Start with classical harmony theroy and work through Max Reger's Modulation. That will go a long way.
Studying actual scores for pieces that you really like. Why? Because the lead sheet don't tell the whole story. Like I said, these are cliff notes and you need to know the story to benefit from them. These scores tell the story of the piece as the composer intended it. Especially for Big Band pieces. This will give you a context for the song allowing you to add the necessary nuances to properly and faithfully represent the piece, or provide a comparative backdrop for your own interpretation. Even if you want to do a bosa nova version of Caravan by Duke or a Bop version of How Insensitive, you have some context that would help to quote the original piece. Lastly, sometimes the backing sections have very cool riffs in them that you can lift and use in performance and soloing. This tells people you know your sh!t.
Listening to multiple arrangements of the same tune by great band leaders and artists. Why? Because you like music and these are good musicians? Music is sound and it helps to hear it. People from different times and cultures will interpret classic pieces differently and you learn by listening to masters work ths out. Also, the lead sheets often do not include interesting intros and breaks that are in the score or on the recornding. Sometimes the recorded versions have a little extra improv that you won't find even in an orchetral score.
I'll give an example uing a simple yet effective Jazz tune, All Blues by Miles Davis. Just reading it straight from the Real Book and having never heard it before a young musician might thing "Hey it's blues so I'll just play a Texas Shuffle, or B. B. King riff". It might work if the rest of the band is on the same wavelength and the audience isn't picky. But the tune is so iconic it is hard to deviate from it and sound good. Enter the Mambo Kings who did a phenominal Latin verion of this. Other great renditions for guitarists are Kenny Burrell on Laid Back, and Pat Martino Live and Yoshi's. Lastly Stanley Clarke Like at the Greek. When I wanted to really learn this piece inside and out I made a "mixed tape" with 12 versions including Miles, and transcribebd all of the Miles verion on Kind of Blue, Piano parts and solos included. This is how you really learn a tune.
Once you've deveoted that kind of effort to at least some tunes you can go back to the Real Book and read through it with a differnet perspective. You can hear the differnece when someone plays down a chart as a novice versus someone who has gone deep into the music. These approaches apply to any style, Bluegrass, Counrty, Irish Folk, Flamenco. It also applies to sub-genres. For example, Be Bop is considered a form of Jazz but Parker and Dizzy are quite a bit different compared to Glenn Miller or Benny Goodman. Don't just buy anthology after anthology, learn the style. Then the anthology will be more usefull. But when you need a huge collection of cheat sheets they are all the same, watered down and lacking in info.
That being said, again, you haven't shared your intent. I always advise studnts interested in Jazz, or any style, to do more listening than reading. If you are a working musician and need to get your hands on the largest collection of tunes keep in mide a few things. The "Real Book" was meant to cover classic Jazz tunes including bop. There is a lot of Duke, Parker, Mingus, Show tunes from old movies and musicals. Other types of Fake Books are more commercial and cover crooner tunes, movie and TV theme music, and probably go deeper into modern Jazz and easy listening, sometime getting into classic rock. A larger fake book like the World's Greatest will be more diverse in pop styles but even more watered down than the Real Book. For me, I like bop and mingus quite a bit. I have gone very deep in learning both with a combination of the real book and listening to the artists. I have every CD I can find with Mingus' work, and the Charlie Parker Omnibook which has his solos transcribbed. I regularly play Anthroplogy, Blues for Alice, Donna Lee, Ornitholoy, Dexterity, and Confirmation. The basic head and changes I did get from the Real Book, but suplemented these with riffs from the CDs and the Omnibook.
In closing my advice is to go deeper with the books you have and if you have already done that, use what you've learned on Real Book Vol 2. There are a lot of great tunes in there.
***** EDIT *****
Based on feedback from the OP I have to add the following. w/r to playing over changes for practice an option is something along the lines of Jamey Abersold play along CDs (tapes or LPs depending on your age), and I'm sure by now they have an online subscription service (if not they should). There is also band in a box, and you can get the complete Real Book vol 1 for it. It is easy enough to input changes. At least this gives you some ear candy, and you can change tempo and style.