Hello HaloReach1827 ! Welcome to the forum! You have asked a very common question. Unfortunately, the answer is vague and ambiguous.
Each of the listed methods have pros and cons. Each can be used to get extremely fine details and beautiful look to armor. It comes down to how good you are with each method, how good your model/patterns are, and how much time you want to invest.
Personally, I think 3d printing would probably get the most detail, but it depends on having excellent models, a high quality machine, and perfected settings (among other things). Pepakura gets hit for not being very detailed but I haven't had a problem with it on my ODST. foam is good for detail but you build it in layers. My personal issue with foam is that if your cuts aren't perfectly straight it is super obvious and (in my opinion) looks bad. Foam is cheap and easy to work with, though and so if you're learning you can make a bunch of "bad" pieces without spending to much money while learning.
At the end of the day your choice of medium has more to do with your time, budget, and experience than with the level of detail you are trying to achieve. There is some gorgeous armor that looks real AF and has crazy detail made through each of the methods. There are also armors made by each of these methods that look less than perfect (my ODST has pieces that look amazing and some that really don't).
I hope this information is helpful. I love watching builds from the beginning so I hope you make a thread and start a build!
As always, don't be afraid to ask questions and try stuff!
If you're wondering about details and looks then the material to use would be... pretty much anything! You could make an incredibly realistic helmet from cardboard or paper mache really - the only thing to think about is how much time are you willing to invest into making it detailed and clean.
3D printing allows a printer to take care of most of the details, but as FalseShepard said, a big part of that comes to how in-tune your printer settings are. On top of that, post-processing (sanding, filling, sanding, filling, etc). can take a long time to make it top-notch.
Foam has a lot of give to it, with how easy it is to manipulate and fix mistakes. There are a lot of different techniques and tips on how to create textures and details.
I haven't done much Pepakura, but for someone who is a bit shaky in the hands fine details can be complex for me, though I've seen plenty of others who have nailed tiny features.
I think the better question to ask would be which method would you prefer working with, such as what sort of materials/tools do you like working with and what do you have access to.