Having done both kinds of programs, here are a few considerations off the top of my head:
When I think about a program, I don't focus on the metabolic effects (hypertrophy, fat loss, mitochondria, or what have you). I focus on the specific parameters of the program: what I'm going to be practicing and trying to get better at. Notice that none of the points below address which type of program would be "better" for hypertrophy, fat loss, or any other physiological effect.
The Giant focuses on the C&P. That means it's a good program if you want to work on the C&P. Yes, if you have hypertrophy or fat loss goals, The Giant can help achieve them, but the means is practicing the C&P. So if you enjoy the C&P, and want to get better at it, The Giant is a good choice. You can really focus on refining your technique and making each set as strong and technically perfect as you can.
Since it's autoregulated, and there are a lot of variations within The Giant, it's also a program that you can sustain over long periods of time. In Dan John's terms, it's more of a park bench program, where you can cruise along and keep making progress (not always linear, but generally upward) over time.
A disadvantage of The Giant is that since you are putting so much focus into the C&P, you have to be more moderate or minimalist in doing other stuff you might also want to practice. It certainly can be done (and I believe Easy Muscle is partly intended to address this), but it takes a little thought, and it's not an integral part of the program.
When you start adding exercises to complexes, you lose the focus on any one drill that you might want to improve. You'll probably have to drop down in weight, and you'll probably be fighting through fatigue on a lot of your sets.
One advantage of complexes is that they spread out the fatigue, so you can do a lot of work in less time. They are a great way to build work capacity, and even though you might be using lighter weights, my experience is that due to the time under tension, you still retain a lot of whatever top end strength you already had.
Since complexes hit a bunch of different movements at once, you can get your cleans, presses, snatches, squats, or whatever the complex includes all in one program.
One disadvantage of complexes is that they tend to be very fatiguing to do. Subjectively, this can be great if you want that challenge, or a drawback if you don't want every session to be a fight. It also means that you might not have a lot of energy or recovery capacity to do much else outside the complexes themselves. The complexes themselves might include more variety than The Giant, but I think there is generally less leeway to add additional variety on top of the complexes.
IMO, complexes tend to be more of a bus bench type of program, one you do for a limited time (which doesn't have to be very short -- Kettlebell Muscle, for example, is 12 weeks), on a more structured progression schedule.
Hope this helps.