I play both steel and nylon string guitar.
All my nylon stringers have the standard flat classical fretboard, with at least 2" (ca. 50-52mm) width at the nut. My acoustic steel string guitars, on the other hand, vary over a wider range: 1 3/4" to 1 13/16", to 1 7/8".
Here's what I find:
In addition to the nut width, the overall feel of each is very dependent on additional "geometry" features of the guitar, in particular the shape of the neck and the string spacing at the saddle. Fretboard width from the nut to the bridge and its radius are also variables which might come into play.
So, back to your question:
Imo, if you were to play identical guitars, safe for the nut width, the 1/16" would indeed matter. I'm pretty sure you would sense it.
But, it doesn't necessarily translate to a different kind of guitar. In other words, a steel string guitar with a nut width of 1 3/4" may actually feel just as roomy if not roomier than a guitar with a 1 13/16" nut width, if overall string spacing, radius and neck shape happen to be markedly different in both guitars.
I hope that makes sense. I guess what I'm saying is that there's more variability in steel string guitars in this regard, and that should be taken into consideration.