For me, it's kind of hard to answer that question in typing (and I majored in Creative Writing, so you know it's hard

). The two aren't so vastly different that it feels like going to Universal and then Disney, but they aren't mirror opposites of each other, either. And the magic is kind of different at both parks, too. It's hard to explain.
I grew up going to WDW, and went to DLR for the first time in 2008 and again in 2011. Leading up to my trip in 2008, I had done a lot of research on the park and its rides and how it came to be and all of this stuff, and knowing all of that stuff I could definitely feel a magical awareness that Walt had been there. Since it was my first visit, I was more aware of everything, trying to scope out every single detail I could. I definitely get what you mean by it having a vintage-y feel!
Walt Disney World's magic is a little different, but it's still vast and immense. Like I said, it's really, really hard for me to put it into words, but it definitely exists. I've been to WDW 6 times not including my last CP, and yet every time I go I still find little things that I had never experienced before, like little details or hidden spots or whatever else. And having worked at a resort, I can tell you the magic is EVERYWHERE (even a little value resort like the All Stars).
To further summarize what Joanna said, we'll put it this way: WDW and DLR's Main Streets were both modeled after two different time periods, so while they look similar in pictures, they still retain their own feeling once you actually get there. WDW has more room to move around, and there's a lot more to do there just because there's so much more land, so you have all these Resorts and water parks and Downtown Disney (which is basically a whole other park compared to the one at
Disneyland). After a certain point comparing the two parks starts like feeling comparing apples to oranges. They're so alike and yet so different. They share some of the same rides, and yet those rides that they share (Star Tours, it's a small world, Little Mermaid, Tower of Terror, etc.) each have their own little things that make them unique.
Even though WDW is way bigger, it's still magical!
If you're curious because you don't know which one you want to try for the CP, you can always go for both when you apply and see from there.