What are the pros and cons of Quantum Armor and the Modular Powersuits?

Short answer being they are both equal, but power suit will better suit your requests(in my opinion)

Quantum offers more protections and a handful of bonuses

Power suits offer SLIGHTLY less protections but can do a whole lot more.

long answer:

Quantum boots let you jump higher and they negate fall damage. Power boots can also negate fall damage, and give you more jump height (in the form of jetboots. They do essentially the same thing, just differently.

Another similar difference is the helmets. Both quantum and Power will let you breathe underwater and keep you fed, but power helmets also gives nightvision(increasing survivability in dark places) and thaumic vision, while the quantum's difference is it protects you from curses (like withering and poison).

If you want mobility, then power suit is the way to go. Quantum only offers jump height and run speed (unless you make gravi suit, which is not easy at all, and power suit does the exact same thing for much less). power suit offers creative mode flight, stepping power(you automatically step up when its a one block height), faster swimming, and teleportation.

Protections... this contest goes to quantum, although power suit can be modified to take very little damage per hit(not even half a heart most of the time), quantum chestplate negates all damage as long as it has power. The quantum helmet is also better suited for fighting things like wither and cave spiders, as it negates curse effects.

Energy use and cosumption with the quantum is cut and dry, but when using the power suit it's an entirely different animal. Basically, the larger capacity batteries you put in the power suit, the slower you will move (the amount is negligible at top tier, though). Also, power suits will charge with basically any form of energy whereas quantum only works off of EU.

It all boils down to preference, but since you are using gregtech I would lean towards Power suits because you would be able to 'finish' it much faster than quantum.

You could mix the 2, like power boots and legs for mobility, but quantum helmet and chest for protections. That sounds like the best option.

pre-reqs and recipes are better found in-game using NEI.