DFRPG has more mechanics, which each individually accomplish less.
DFRPG is a lot crunchier. Although it maintains the "players can make up their own setting and features" ethos that is the hallmark of Fate, it has a LOT of subsystems in which to do this. For example, it provides a solid and complicated magic subsystem. You're free to make up your own spells and schools and so forth, but the rules those things function within are set.
By contrast, Core does everything it can to prune away subsystems. It's left with a handful of mechanics so robust that you hardly need to create subsystems at all, although it provides guidance on how to do so if you want to make a magic system or the like:
Whereas each previous Fate game had a specific way of dealing with powers and gadgets and stuff, now there are a variety of options for you to choose from (as befits the toolkit nature of the system). (FC 294)
This means it is possible to imagine a group using the Fate Core manual to come up with DFRPG on their own, using the guidelines to create a vast number of extras and fractals, but it's unlikely: a lot of DFRPG's "narrow" mechanics are filling a void that Fate Core later filled in by making the main mechanics wider.
Vocabulary and mechanical tightening-up
DFRPG has a relatively unnecessary sprawl of specialized mechanics, some of which aren't defined particularly well. Core rolled many of them up into a handful of more robust mechanics that filled the same function:
Movement is now a function of the overcome action, create an advantage subsumes assess/declare/maneuver from previous games under one banner, and blocks can be handled a number of different ways[,... and] zone borders have been replaced by the use of situation aspects[....] (FC 294)
In that spirit, action economy is greatly simplified: supplemental actions are gone and free actions simplified. Most turns in an exchange consist of a single action.
The same is true of Fate vocabulary. Core boiled DFRPG's half-dozen different kinds of compels and invokes down into invoke and compel (event compel and decision compel are subcategories of compel, but they're more for clarity of intent than a mechanical distinction). Likewise, the specialized word "tag" for free invocations was excised as needless jargon when "free invocation" works just as well.
DFRPG's established subsystems may make it a more comfortable system for a player with D&D-like prior experiences to break into Fate, and it's certainly going to provide more opportunities for mixing and matching pre-designed options instead of making your own.
There's also a distinct difference in the tone and quality of the manuals: DFRPG's text is chatty and rambling, great for giving setting atmosphere but not so good for presenting the rules unambiguously and being easy to flip through for reference at the table. Fate Core's text is still informal, but it's also precise and concise, and beautifully referenced.