I think they are just presenting that argument badly.
I have complained that 4e defenders sharing a marking mechanic makes them samey. The same mechanic across different classes does add to sameyness on the cross class level. I'm willing to acknowledge that. Are you?
However, to answer the criticism. 5e's differentiation of Barbarians/Rangers/Fighters/Monks/Paladin's primarily comes through in their level 1-3 class abilities. To me that's a much larger differentiation than 4e provided them, at least in the general sense (can always cherry pick a few powers that may be sufficiently different - but that's the exception not the norm) - which is why to me 5e feels much less samey than 4e.
But, doesn't that lead into what I was saying - that many of the things that 4e would present as "powers" are simply rolled into a single entry and thus, in 5e, it makes the classes look more differentiated?
After all, by level 3, what actually differentiates a fighter from a paladin or a ranger? They have the same armor, same weapons, same fighting styles. A paladin has lay on hands and 2 spells per day and a ranger has nature sense and 2 spells per day. Our fighter has Second Wind and Action Surge.
In play, round by round, those three characters are going to be doing a LOT of the same things over and over again. Yes, there will be a few rounds they might be different, but, overall? Most of the rounds in combat, they won't do anything different at all.
Never minding the first three levels of full casters. It's entirely possible to make two different classed casters have exactly the same spells.
I'm having a pretty big difficulty understanding this. The difference between 2 level 3 4e characters is considerably larger than the difference between 2 level 3 5e characters simply by virtue of the fact that those two 4e characters each have a choice of about 30 different powers by 3rd level. The odds of those two characters looking anything alike is actually pretty slim unless it's intentional.