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They vary, and they seem to vary much more than "slightly"... I saw it mentioned on another forum that the average 4/4 violin neck width has increased over time, though the necks of new violins seem to vary greatly at any particular time too.
My 1950s German workshop violin has one of the widest violin necks I've seen, almost as wide as the neck on my viola.
Interesting.... I only have violins ( 5 of them ) but (and no I haven't measured them) - but - of the 5, one happens to be a 3/4 size fiddle about 100 years old - a "mass produced replica thing" - I got off e-bay (initially purchased for taking apart and practicing some luthiery - but - with a little bit of TLC she was actually really playable, with her own quite unique voice - anyway I digress) - however - it is quite clear to me that on that 3/4 mass produced, virtually worthless to anyone but myself - the neck is ( appears/feels/probably-is to me to be ) both thinner and narrower... The "narrower" may just come down to a few mm difference between string separation on the nut, but I do notice that fingering needs to be that "little bit more precise" to avoid accidentally damping an adjacent string...
I kind of suspect that @AndrewH has said it really - they're gonna vary - unless it is constructed to some (probably non existent special-measurement-formula - OK - I know there are "specifications" - all I mean is - they are not always followed....)
That probably doesn't help the OP question @Mouse - just my observations as a player!
I seriously recommend not copying my mistakes. D'oh -
Please make your own, different mistakes, and help us all learn :-)