If you want it to be a complete, stand-alone game then you should include the full book rules. On the other hand, if you want it to be a supplement then only include the new stuff you're doing.
Add the Entire Core Rules If…
…you want it to be a stand-alone game
If you don't like the idea of "Requires a Copy of Fate Core System to play" being in your game, include the entire rules.
…it's intended to target non-Fate players
Fate gamers already have the core rules—usually several copies of them between the online SRD and the various stand-alone Fate games. If your target audience isn't the entrenched Fate community, including the rules is a good idea so your customers don't need to purchase two books when one will suffice.
…the rules changes are so massive it makes more sense to reprint everything
Some games futz so much with the core rules that listing the changes is almost synonymous with reprinting the core rules. A game that I recently finished writing (still in layout stage) completely removed the contest mechanics and replaced them with a modified contest mechanic and replaced skills with ranked aspects. Because of these major changes, we opted to reprint the rules with the new changes in mind.
…you want a bigger book
Let's face it, sometimes you just want to hold a hefty tome. If your rules tweaks and setting material only cover 32 pages, adding the rules into it will increase the page count by 200+. The physical feeling can be satisfying.
An Evil Hat example: Atomic Robo is a stand-alone game, and thus has the entirety of the rules held within. It's designed to attract the comic fans into trying RPGs.
Exclude the Entire Core Rules If…
…the rules changes are small
Small rules tweaks doesn't require the reprinting of the rules. Just a few pages to note the difference and you're good to go.
…you are targeting the Fate community
Between the core book, Atomic Robo, Bulldogs!, and the SRD, I have more copies of the rules then I need. I don't want them reprinted yet again. And many other Fate gamers are in the same boat.
…you want an affordable/binge purchase price
A higher page count (both physical and digital) means a higher sticker price. Art, layout, proofreading, and all the other expenses besides printing costs are usually based off of page count or word count. Less pages and words means less expense to make them look great on the page/screen. Also, smaller page count means the printing costs are less.
Another Evil Hat Example: The Fate Worlds line from their Patreon. Each setting only has the new rules/tweaks and setting included. The Worlds of Adventure are for the existing Fate community, and therefore don't need the rules reprinted time and again.
How Do You See Your Product?
In the end, there is no "right answer" to your questions. You have to think about how you want to market your product(s), who your target audience is, and how you want it/them to interact with the growing Fate library.