Something interesting I want to note right quick about "feelz" versus design.
4e and Moldvay Basic are (IME - which is correct) the most tightly designed editions of D&D. They each have an explicit premise (MB as well-oiled, after map/key are created, nearly self-sustained content generating dungeon crawling machine...4e being closed scene resolution, player-driven, high octane action adventure centered around destined heroes ensconced in mythical conflict). Their build and resolution mechanics are "outcome-based" (engineered toward their respective premise) rather than attempting to model process.
Map/key + Role-centered classes + Exploration turns/rest + Wandering Monsters + Encounters + Reaction Adjustment. And all related.
Action Scenes charged with PC-centered conflict (from combat to parley to rooftop chase to escape from crumbling complex to infiltration/espionage to esoteric research to perilous journey, etc etc) + dynamic decision-points + universal narrative authority + scene resolution mechanics + failure isn't an endpoint.
Play snowballs naturally and premise-coherently in both systems.
But the "feelz" are rather different due to divergent premise. Nonetheless, they're still both very much D&D. And they both diverge in certain key ways from AD&D and 3.x (process-modeling rather than outcome-based design is a big area where they diverge from 3.x...universal narrative authority vs spellcaster exclusively, go to the action vs serial exploration, and scene resolution are areas where 4e diverges from both).
Resultantly, I would put Moldvay Basic MUCH CLOSER in the D&D family tree to 4e than to the others.
One final note to @
Parmandur. I think when you're trying to compare the D&D board games to 4e, you're rather showing your lack of familiarity. See my above. If anything, it's probably closer to a Moldvay Basic dungeon generator (where the map and key are generated at the moment of play). It has the basic exploration procedures (less Reaction) of Moldvay at its core. The only thing I can see it shares with actual 4e is VERY rough combat action economy, vanilla class features, and everyone has Dailies. If anything, it is an extraordinarily shallow mash-up of the two (which it isn't...sooo). And of course, most importantly, MB and 4e aren't board games. They're both actual RPGs where the shared, evolving fiction is the primary input for expansive play/action declaration & resolution (hat tip @
pemerton for robust, concise definition).