I only have concert and sopranos, but yes, I would say yes each larger size has a wider fret board and more frets. But maybe you need to hear from someone smarter than me.
The fret spacing ( space between frets) is longer, thus even on frets past #10 or #12, there's more room for fingers. BUT, the width (across the neck/fret) isn't necessarily dramatically wider on soprano to tenor. I have all sizes & that width varies most from maker to maker rather than uke size. For example, my soprano, longneck soprano, & tenor scale KoAloha's have a wider neck than my tenor LoPrinzi. And I've owned a concert Mele which are known for narrow necks.