It started with The Sundering modules. The modules described the story, the characters involved and the setting, and provided a lot of information for the Dungeon Master. The rules of the game were pushed into downloadable PDFs that made the module compatible with D&D Next, D&D 4th Edition and D&D 3.5 Edition at once.
The idea that a module can consist solely of story elements and still fill 30+ pages (or triple that number - see Hoard of the Dragon Queen adventure module) means that rules take the backstage and the characters, the players and their actions through the evolving story is what's matters the most.
That said - a simple ruleset often means more work for the Dungeon Master, as players try to do things not covered by the rules, requiring the DM to make judgement calls all over the scenario. In addition, simple rules sometimes mean simple characters, with players unhappy with the few options the rules provide for character development.
So I looked at Fighter class and compared the Basic D&D version of it to the 5th Edition version of it, reasoning that the Fighter class had always been a 'simple' choice, and the default one for new players joining an existing party.
Basic D&D described the Fighter in a single page, summarizing the class by saying that "Fighters need no special abilities to survive and prosper. Their great strength, hit points, strong armor and many weapons make them a powerful character class."
In Basic D&D, playing a Fighter was easy rules-wise. Tell the DM what you want to hit, roll a die, and hope for the best. That's it. The first 3 levels didn't include any special feature or maneuver - these came after level 4, but summed up to some fighting abilities using lances and spears. The Fighter was designed to be durable, that's it. Players often steered off of the Fighter class, and only exceptional players could bring a Fighter character into life.
In 5th Edition, the Fighter's description is spread over 4 pages, with each level adding some feature or ability the player can use. The Fighter is still designed for durability, but it now had some interesting options the player could use to gain the upper hand in battle. The Fighter main functionality remained the same: pick a target, roll a die - but now the player could put things like Action Surge, Fighting Style and Martial Archetype features into good use.
In addition - 5th Edition now include a whole chapter dedicated to Personality & Background, which helps novice players (and let's admit it - even seasoned ones) to paint a unique picture given a race and class combination. So your "Level 1 Human Fighter" can become Theodar, an Acolyte of the Masked Hive Queen or Sinadi, the half-crazed Hermit living in the Fog Mountains, kickstarting an ocean of possibilities for role-play and social interactions.
It D&D 5th Edition perfect? Probably not. I (as a Dungeon Master) still find Basic D&D simplicity a bless. But I have to admit - creating a character in 5th Edition is interesting, especially if you let in some randomness using the information presented at the Personality and Background chapter. So the system is not Basic D&D simple, but it's definitely not 3.5e complex - I was able to use a random 5th Edition monster stats without taking 15 minutes to read it before session, and I was able to run several 5th Edition sessions without memorizing the Player's Handbook.
Moreover - I find the module design (I currently own all the Sundering modules and Hoard of the Dragon Queen) very DM friendly and story oriented. Again, not perfect - I still cringe when 'high-level' NPCs send the player characters to do their dirty work for them, but any module containing a list of 20 non story central NPCs your players might interact with during a caravan trip on the Trade Way to Waterdeep is worth owning, reading and using...
I'll wait for the Dungeon Master Guide (and the Monster Manual) for completing my overview of the system - but so far it looks very promising.
Enjoy!
