I have experience with these three, and other Canson papers, with both our ConeColor and Piezography inks. My personal experience and thoughts are as follows:
1. Edition Etching Rag 310 is one of the primary papers we use for color printing at Cone Editions Press. We like this paper (and apparently many of our customers do too!) a lot because it's bright white, OBA free, 100% rag, has a nice smooth texture, produces crisp details and vibrant colors, as well as a deep velvety black, and holds up well when handling (the surface doesn't flake or mar easily, like some other rag and slightly textured papers can often do).
Arches Velin Museum Rag: is available in 250 and 315gsm, I have used the heavier weight, because of personal preference, but I'm sure the 250 wright is just as beautiful. This paper is mould made, as again contains no OBAs. AVM has the same smooth texture like EER, but is slightly warmer. I would say the print quality is equally beautiful with both papers. I don't have a lot of experience with this paper, but have printed and evaluated test prints made on it.
Rag Photographique: available in 210, 310gsm single sided, as well as 220gsm duo-sided. The 310 weight is one of our absolute favorite papers for both color and Piezography, working well with all sort of subjects including portraits, landscapes, architecture, etc... This paper has a beautiful smooth surface, and I would say the whiteness is between EER and AVM. We use this paper a lot, and plan to continue recommending it to everyone looking for an incredible rag paper. This paper takes ink very well for crisp details, vibrant colors and deep blacks like EER, but has a smoother, more photographic look/feel.
If you would like to see printed samples on any or all of these papers, you can order a custom Piezography print of your personal image(s), and make a note in the order specifying the paper(s) you'd like to see.
I hope this helps, please let me know if you have further questions or if there's anything else I can help you with.
Best regards and happy printing~ Dana