Why is that the case? How does 4e lend itself more to story now? What did 4e modules look like? Sorry, very basic questions...I don't have a lot of experience with 4e.
4e modules are, on the whole, awful. Some people like some of the later ones; they may speak up in this thread.
The essence of scene-framed play is this: situation (normally authored, at least to a significant extent and in 4e D&D to a great extent, by the GM) that responds to the players' evinced interests/hooks/thematic concerns (ie while the GM is the one who frames the scene, it is the players who implicitly or explicitly set the stakes); action declarations from the players for their PCs that engage the situation (which they should be able to do by just playing their PCs, assuming the GM has done his/her job properly at the framing stage); typically there is some sort of back-and-forth of success and failure and emerging consequences (this is the rising action); then there is the resolution and pay-off of the scene, which may do any or all of the following: lead to a change in the characters (eg one of my players decided that his dead human wizard, when raised, would return in his "true" form as a deva invoker - but not all changes need be as big as that); lead to a change in the setting (eg now the hags are allies of the PCs rather than enemies; now the djinni are reconciled with the gods rather than getting ready to fight against them in the Dusk War); lead to some new conflict or challenge (eg now that you've defeated Torog, there is no one holding back the Elemental Chaos - oh, and you sealed the Abyss too? So now all that chaotic energy and matter is not getting siphoned down into that well of nothingness, it's just overflowing into the world!)
The framing of the next scene
has to have regard to the fallout from the previous scene. Otherwise it wasn't really fallout, it was just meaningless froth and bubble. But the approach of the typical D&D module is to ensure that no fallout ever matters - and often within a story before framework, so (eg) if the PCs kill a particular antagonist early, the GM has advice on how to keep the villains going in any event, or if the PCs miss a crucial clue the GM has advice on how to make sure they get the information in any event, etc.
The 4e modules I own are mostly like this. I used bits and pieces of them for maps, characters, stat blocks, and ideas for particular scenes or antagonists. But not as written.
The single best 4e adventure I used was Heathen, from one of the early - and free - 4e-era Dungeon magazines. I cut away some of the cruft. But in its basic structure it resembled the excellent Prince Valiant episode The Crimson Bull - which is the best example I know of a multi-site, multi-event scenario for a scene-framing-based game.
The core structure of both these scenarios is to use the early episodes to reveal aspects of the antagonist, and elements of the stakes, so that in structural terms they form part of the framing of the final climactic scene even though - in the fiction - they occur at earlier times and places.
Anyway, on the back of that account of how scene-framed play works, here is why 4e lends itself to it: most PCs have rich hooks built in which the GM can respond to in framing scenes (as I said, there are some exceptions - archer rangers don't bring much energy to the table by default, and I think halflings are the same of the PHB races); the mechanics give the players a lot of capacity to impose their will on the fiction through robust action declarations that really make things happen and with little to no GM gatekeeping; and there is tight scene-based resolution for both combat and non-combat (skill challenges are the key mechanic for the latter).
If you look at the thread I linked to earlier -
D&D 4E - Pemertonian Scene-Framing; A Good Approach to D&D 4e - you can see all this discussed in quite a bit more detail.