There is a lot of info on these sticks and the Xbox sticks, but nothing that says exactly how close they are.
What are you talking about?
I've done tear-downs of the sticks Arcade VOOT sticks:
http://solid-orange.com/1229
My friend Lee did a tear-down of the Hori (Xbox 360/PS3) sticks:
https://twitter.com/VOTwinstick/status/488167939955113985
Also a comparison I did of the various official arcade sticks:
https://www.oratan.com/forum/viewtopic.php?t=1491
I have all the different revision of the Arcade VOOT and Force Sticks as well as the Candy OMG sticks, the twin unit OMG sticks the Dreamcast Sticks, as well as the generic Sanwa and Semitsu replacements. the only ones I don't have in my possession are the Saturn sticks and the Hori sticks
at some point I plan to do a an in-dept comparison between them all. However I've written numerous posts here about the differences between the sticks here:
$800 for a pair of VOOT carts!? and else where on the forum.
in terms of the grip shape the Arcade VOOT/VOF (also used on Outtrigger and Gundam Battle Operation Simulator), Sega Saturn, Dreamcast, Xbox 360 and PS3 all have identical grips in terms of the outisde feel (they're all different internally and incompatible with each other), the rest have different shaped grips, and they all have slightly different mechanical feel to them.
A brief overview from best to worst:
Arcade VOOT/VOF, and Hori (Xbox 360 and PS3) are the best sticks they have a really robust design, they're very accurate they mount properly to an arcade panel and they have the correct grip shape. Hori sticks are black, while the authentic arcade sticks are a charcoal gray color, maybe that matters to you?
The Sanwa and Seimitsu generic replacements are really good sticks in terms of their mechanical design, and they're all designed to mount to a proper arcade Panel but they have different shaped (less ergonomic) grips... so not as authentic but maybe that doesn't matter to you.
The OMG Twin unit sticks are made by HAPP - these things are built like a tank and could survive nuclear fallout, the grips are "authentic" but they're not the same as the VOOT grips, these sticks are ENORMOUS and they WILL NOT fit inside a candy cabinet panel, they're also heavy so they're a little slow to use on faster games like VOOT (I currently use these sticks in my cab and I still own punks though

)
Dreamcast sticks are made Seimitsu they have the authentic grip shape but they're light gray with orange buttons to match the Dreamcast's color theme. there is no proper mounting plate for a panel and while they're precise sticks they're pretty cheap/flimsy, not arcade quality.
Saturn sticks are made by Ascii and are even more cheap/flimsy and the Dreamcast, they wont hold up to abuse and again, no proper panel mount. These are the cheapest sticks you can buy though and the grip design is correct. They're a little darker than the arcade VOOT sticks but otherwise the closest color match to the real grips
OMG Candy sticks are more robust than the Dreamcast or Saturn sticks but are really total garbage in terms of feel, also has the worst grips of any stick available... these are based on Sanwa JLWs and honestly Sanwa should be ashamed.