Yeah, I'm with Pour, I have NO IDEA what you mean by this. I don't know what 'both styles' you refer to. In 4e, IF YOU WISH, you may of course make NPCs using PC classes, nothing can stop you from doing this. There is even a simplified method of doing it in the back of the DMG (in chapter 10 I believe, right after the monster design rules).
I'm not 100% sure but I believe he means the mechanics-first design of 4e versus much of the story-based design of earlier editions.
4e designed around the basis of the mechanic. As always, there are exceptions and there was quite often a story-kernel at the basis of the design, but it was often much narrower than the role of the class in the larger world.
The warlord is one example of this, being designed first and foremost around the concept of the martial leader that can grant attacks, damage, and movement while also healing. When you describe a warlord first and foremost you describe what he does in combat and his mechanics.
Ditto the avenger which was based around the oath mechanic, the idea of a Batman character that fights alone while being part of a team, and the visual of a lightly armoured sword wielder.
5e is starting with the story first, describing what the class is in the world, what its role is, how it is unique and then looking at mechanics. Or so we've been told.
When you start with the story, you'll always get a good world hook. And there's nothing preventing you from making equally unique mechanics and designing an awesome class.
When you start with the mechanics first, sometimes you're going to get a good world hook and sometimes you're not. Few of the 4e classes really stand out for their flavour. The battlemind is a mass of story contradictions completely divorced from its flavour. The seeker and runepriest overlap with the ranger and the cleric. The battlerager fighter should have been a defender barbarian.
But I disagree with GX.Sigma that mechanics first cannot lead to good story and classes. I thought the swordmage worked fine, and the warlord does still deserve to be it's own class.
In fact D&D was invented as a game of dungeon exploration. No greater 'world' than "the town" where you could buy supplies ALA Diablo (the original game with the hard-coded town) was envisaged by those rules, and the game up to 4e didn't really change those assumptions much at all. No thought was ever given to how the world was supposed to work. The few parts of it the PCs were ever expected to interact with were just given as hard and fast rules, prices, hirelings, followers, castles, etc were all simply hard-coded in the DMG "this is how it works" with numbers of gold pieces and etc and NO explanation of how that could possibly be logical when you considered the implications of even level 1-3 spells.
Chainmail was a game of dungeon exploration. D&D was that for thirty seconds and quickly evolved. It did not take long for D&D to move beyond the dungeon, for worlds to grow larger and grander. For people to start questioning how the world the mechanics were creating might actually work and interact.
And while the game was simple now, you can't go back to that. The genie is long out of the bottle and people do wonder how classes interact and affect and alter the world. The world consequences of clerics with cure spells has been known for twenty-five years and was part of the basis of the original
Dragonlance world. We cannot design like it was 1974 anymore.