They give a very good impression of the setting, and they also give a pretty good background for understanding how the rules work.
The game was designed to very closely emulate the fiction of the books (Evil Hat and the author worked closely together for about a decade, and much of Evil Hat's work on developing and refining Fate over the years and multiple products has been intended to get "good enough" to do the Dresdenverse justice), and knowing the fiction will help understand much of the game design, especially the magic subsystem and the overall "feel" that the game's rules engender.
Another point in favour of reading the fiction is that the rules as presented are not exhaustive – the rules give you lots of leeway to come up with your own character templates, creatures, rituals, and the like. Having read the books will give you more of a grip on the world so that you can more easily make stuff that enhances the game.
I would say that reading one or more of the novels is strongly recommended, but not strictly necessary. You can still enjoy DFRPG a lot without knowing the books, and the rules do come with a lot of embedded flavour (especially if you also have Our World), so you can absorb sufficient fiction from the rule books alone.
That said, if you are getting the RPG in order to pick apart and understand Fate, it's not necessary to read the fiction. DFRPG is an excellent instantiation of Fate, and as I understand it, is the closest incarnation to the next generic version of Fate in Fate Core. However, even then you'll understand the raison d'être of much of the rules better if you know at least something of the fiction it is inspired by and attempting to support.
I don't think you have to hide the numbers for what you are doing, but rather just how you get them.
I've made my game more player facing, i.e. they players roll all of the dice. But I've also made it more narratively driven, i.e. the players don't invoke their powers, instead, they describe their actions. (Taken liberally from *World games)
I did this in response to exactly the problem that you're having- that DFRPG can be overwhelming at times. So how does this work?
The first part about the GM not rolling takes a lot off of the GM's shoulders, and makes things faster. You then use this savings to spend the time to interpret the players' actions, and trigger them based on the narrative for the players that are less familiar with the rules. Rotes help a lot with this.
So, the only things you have to explain to your player are- the rotes that you help them design with their characters, and the meaning of overcasting vs standard casting. Once you've done that, the player describes what they are doing, i.e. casting their rote, or putting more effort into it or really pushing themselves. You look at the numbers behind the scene, and give them the target. They roll... and describe what they are doing to invoke their aspects as needed, since they know what they need to make the roll.
This way, they are eased into the aspects of the game that have to do with Fate, while the crunchy things of magical manipulation are kept behind the scenes.
In summary, let them describe it in the narrative, you do the heavy lifting, then let them roll against a static number, invoking aspects as needed to make the roll if they want to so with more narration.
Best Answer
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:
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:
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.
Other thoughts
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.