I like a neck that just fills the palm of my hand when I do a thumb over barre chord. Too small and I tend to get cramps in my hand, too large and the neck gets in the way. IMO, a guitar neck is like a pair of shoes...you just have to find a comfy fit.
I think comfort is a personal thing and speed has nothing to do with the size of the neck. I can't play a thin neck without having my hand cramp up after a short time, so bigger is better for me. Any speed differences i have come from practicing, and for me, speed is generally limited by my picking hand rather than my fretting hand.
I don't know about facts, but how about some opinions?
The fatness of the neck has several impacts to me.
IMHO a neck with some volume stands an excellent chance of transmitting a lot of string energy to the pickups and body of the instrument. There are always exceptions of course. But maybe some volume left in the carve of a neck, adds stiffness, and makes for a sound that's really full and appealing, whereas perhaps the same stick of lumber further shaved, might be underwhelming? Just an opinion.
I have at theory that a generous back shape offers support to the fretting hand that a flatter neck carve lacks. So longer hours of less fatigued playing are the result. Everybody has different hands and postures, so results vary.
A fatter neck often is a companion to a roomy fingerboard. This is one issue I have run into with some classic Fender necks. The taper of certain Fenders seems sort of congested for me down at the nut area.
I'm not dogmatic about any of these ideas. For instance one of my guitars, a mid sixties Epiphone Sorrento has a really skinny neck, and sounds amazing. Part of the reason is the wood selection, super dense Mahogany with the grain flash that some of those old Gibsons have, plus the added mass of the extended Epiphone headstock, but that neck is really nice.
I think the grain of maple necks is a big factor. Adam Stark pointed out to me that a lot of the ridiculous wonderful Fenders of various eras, seem to have grain patterns that are widely spaced and not figured or flamed particularly. Check it out in your travels and see if you agree?
For the last decade or so , it's certainly trendy to like large necks. In the 80's it was about as slim as you could get. I've always, well since '91 anyhow, liked my '66 strat neck. It's chunky C but not huge and just fits like a glove. Spoils me from just about any new Fender.
I've had strats where I stuck on an SMO Fat Allparts, or a fat USACG, neck on it and it did not sound better than the skinnier one that was on it before. I've done that experiment at least three different times with different strats and never noticed an improvement in tone. I thought it would add more resonance since there's more wood. It just didn't happen.
When we get done here, maybe we can come up with some factual advantages of pilsners vs. IPA's.
Peoples hands and how they use them are different. Try different things out, figure out what you like, and go with that. Not much more to it than that in my experience.
As to which may be faster, I've done a number of experiments dropping different shape necks off my roof, but the results have been inconclusive. Far as I can tell, even though a player may be able to move around faster on whatever neck is most comfortable to them (whether it be thick or thin, flat or "V"), the necks themselves all seem to hit the ground at about the same time.
There are no hard rules. In my opinion, the best thing you can do is just try different stuff out and see what works best for you.
If I ran a high end shop and took custom orders guitar-fitting would be at the top of my sales pitch, just as golf shops offer custom fitting.
Sure, standard is close enough for most people, but if you are off-standard wouldn't it be nice to know your personal specifications are optimized?
In fact, anyone might benefit from a thorough assessment of their hand size, flexibility, technique and then be tested and fitted appropriately. Make it right, add value, upcharge $$.
I probably sell more FAT "U" profile Tele necks than anything. I'm not a big fan of them, but LOTS of people swear by them. I guess it all depends on what you're used to. I don't have the largest hands so I tend to prefer the "V" profile necks. I owned a few FAT necks and I just never could get used to it. I don't think that there are any pros or cons - just a matter of personal taste.