Folding rules come in two main styles: inside read (also called "English measure") and outside read ("American measure").
I've never found a good, verifiable, explanation for the difference. There is a rumour (that I think is unfounded) that the American measure was standardized in simple opposition to the English measure. That seems overly perverse, even for the complicated relationship the US has had with England.
The English measure is certainly more natural for right-handed people who want to use the rule for layout work, marking out left-to-right, or for measuring inside dimensions. Even left-handed folks like myself still work left-to-right, and in that way that left-handed people adjust to a right-handed world, I prefer laying out left-to-right, using my right hand on the rule, and marking with my dominant hand. Though some left-handed people use an English rule upside down (and, indeed, you can get left-handed versions of both styles).
I've heard that plumbers and, later, electricians, preferred American measure, but (again) this is unfounded. I certainly couldn't tell you why this might be so for those trades.
I think most people who want to revisit folding rules should stick with English measure (inside read) rules, at least for most woodworking. It is the most useful for layout, for measuring rough dimension lumber in a yard, and for general carpentry where you want to measure inside dimensions.
Plumbers and electricians use rules in a different manner, and maybe they don't care that it lays flat; perhaps they prefer that it can unfold easily in the left hand so they can reach into a void while they use their right hand to mark or cut.