While the concept of DL and WDW versions are obviously quite similar, there are a lot of differences that would probably make it a substantial challenge to simply give WDW the same DL enhancements. The ride systems even seem to be somewhat different, DL stops to load/unload guests much like other dark rides while WDW is a continuously moving ride (kind of like an omnimover in a sense).
A lot of the scenes are different as well. The two versions mostly start out in a similar manner, including the nursery scene and the flight over London. There are minor differences, but not too drastic. In fact, it's arguable which London is the better one. DL's has a mostly flat floor texture, whereas WDW uses physical 3D buildings. This is mostly a matter of opinion, DL's actually conveys a higher altitude. I've always liked the 3-dimensional buildings personally, though either opinion is valid.
Once you get past that, the two versions split off considerably. The Neverland island at DL is a smaller one, which is supposed to simulate you at a high altitude. They made WDW's a larger room-filling scene to simulate being closer to the ground. But personally i've never liked how WDW's was handled, for a lot of reasons. Only as an adult do I sort of get what they were going for, but the pacing is off and the areas aren't separated enough. The inclusion of characters into this room (mermaids and Indians) also throws off the forced perspective, they're very disproportionate to the surrounding scenery.
The scenes following however are better put together and could be enhanced more easily, they're closer to the Disneyland version.
It would be somewhat difficult to simply replicate Disneyland's new enhancements given the different flight over Neverland scenes (and the mermaid/indian placements). Even the soundtrack is different. It would take a substantial rebuild to be get WDW in proper shape IMO, requiring a rather lengthy downtime (much longer than a couple of months). It hasn't ever been altered since it opened, Disneyland's was already heavily enhanced in the 1983 rebuild of Fantasyland.
I do recall it being stated not long ago (I think by WDW1974) that Tokyo's version of Peter Pan will probably be upgraded during its Fantasyland Expansion. Tokyo's Peter Pan is an exact clone of WDW's, so it'll be interesting to see how they handle it.