There are a lot of questions that I see related to how to make Fate Core more "this" or "that". They usually revolve around mechanical concerns, probably because in most games that's how you handle enforcing certain things. If you want to make a game more comical, you exaggerate certain elements or restrict things (like removing lethal damage). If you want to make a game more "realistic", you do x, y and z. A lot of this has to do with most games not having other tools to make those kinds of adjustments.
With Fate Core, though, we have aspects - and aspects are at their core language. How aspects are worded, and thus interpreted, can have a huge impact on the game. Humorous aspects reduce how serious the game is, while dour (or even darker) tinged aspects can change the atmosphere dramatically. For example, consider Shaun of the Dead compared to most other zombie apocalypse fiction. Shaun might have the aspect:
Buy Milk. Ring Mum. Dodge Zombies (lifted from one of the taglines of the film)
While in a more serious game, a character might have the aspect:
Survival At Any Cost
The wording sets the tone, and this is true for any of the aspects in the game - character, situation, boosts, campaign, all of them. This isn't to say that there aren't mechanical means to deal with bringing about a particular mood - only that aspects are going to be the linchpin of that effort (and in a lot of cases, not much more will be needed). This extends to how aspects are invoked and compelled. Hostile invokes and cutthroat compels have been suggested as a means of creating a "grittier" (or at least more unfriendly) game. The same goes for any other theme, especially since the wording of the aspects are going to speak to how they are invoked and compelled.
So I guess my point here is when hunting around for ways to tweak out Fate Core, look toward how aspects are worded and what the table wants them to evoke. If that doesn't quite do it then maybe look at other adjustments to the game system. This doesn't necessarily apply just to Fate Core either - how players around the table talk during any game is going to have a major impact on the mood of the game. That's really kind of pointing out the obvious. The difference is that Fate Core (and games that are similar) have the language baked right in.