I used B/X for a reason forbthat specific statement. That ruleset relies much more heavily on procedures and rulings than what's on the character sheet, even compared to AD&D which was significantly crunchier (yes, yes, no one actually played it that way...).Uh ... yeah, I don't think I can agree with this.
Obviously, depending on how you define "differentiate," a person can make a good argument that different classes in 5e have more abilities than they used to. However, that's not really the issue. It's about niche protection.
In B/X (and OD&D/AD&D, which are better example), there was much more niche protection. Let's use AD&D as the example-
If you weren't a thief, you didn't have thief skills.
Weapons and armor were restricted by class. Magic users got daggers, Fighters got two-handed swords. Magic users got not armor, Fighters got plate.
Magic items were also class-specific, to a much greater extent than they are in 5e.
Hit points were less, and therefore the difference mattered a lot more. d4 hit points with minimal constitution as compared to d10 with up to +4 per level.
The highest strength bonuses were restricted to fighters.*
...and so on. So I can't agree with this statement; the amount of differentiation, in terms of niche protection, was much much greater back then.
*When I say fighter, I mean fighter and their subclasses.
A 1st level cleric and first level fighter were almost identical, and a 1st level thief was not to far off. Everyone's hit points were low, everyone's damage potential was low, spells were an extremely limited resource and their abilities weren't much higher than the base 1 in 6 chance used for most actions outside of combat anyway.
My point, though, was that there was not (in my experience) as stark a mode shift between exploration and combat.