I can imagine a few factions and unique mechanics.
Factions
There would be 4 unique factions, each with it's own units and characteristics. There would be the Wastelanders, The Enclave, The Brotherhood of Steel, and the Super Mutants. The Wastelanders would be a "survival" faction, meaning that direct combat with the other factions would have to be avoided in favor of less direct means (guerilla warfare, bombings, etc.) Because they are survivors, their combat units would not be as powerful, but they would have more functions and survivability. Instead of armies, they would produce a few common units (city guards, militias, Regulators), which would be lead by "Hero" units. "Hero"s would be extremely powerful, but rare. They would be found inside vaults, and sometimes be born in settlements. The only way to destroy this faction is to kill all their units. The Enclave faction would be the most conventional factions, with armies consisting of a few varied units with single purposes (less unit functionality). Their combat units would be in the middle of the range in terms of power, but they could have lots of them, more than the other factions (most of the time). Because they gather resources slowly (see below paragraph), it would take more time to build up armies through their bases (see below). There are several ways to destroy the Enclave, either through destroying their bases, killing all their units, or by using a superweapon (superweapons are extremely rare emplacements in the Wasteland, which are one use only, including the orbital strike platform, and atomic artillery). The Brotherhood of Steel faction would also be fairly conventional, with more varied units for different purposes. However, their units are more powerful and expensive to build. The upside of this is that units that gain lots of experience can become very powerful, offsetting the expense involved in making them. They can be killed in several ways: by killing all their units, destroying their bases, or by killing a handful of powerful "Leader" units, who are regular units who have leveled up significantly. Finally, the Super Mutant faction would be the strangest (similar to playing as the barbarians in Civ 4 Warlords). They would start with a few permanent bases, from which they build units by capturing and converting prisoners from other factions (more on this in the "Resources" section). Their units would be few and simple, consisting of Brutes, Masters, and Behemoths, all increases in power over the others. Once their bases are destroyed, they are finished.
Resources
Instead of farming or whatever, you would scavenge. The various factions would have different methods of doing this. The Wastelander faction (consisting of survivors, vault dwellers, and non-feral ghouls) would have units which all could scavenge for resources. Scavenging would be a luck-based action, with the odds of a good haul increasing with unit level. They would be able to scavenge from dead enemies, and the higher-level ones can scavenge from certain ruins (which would have a greater haul, but also a greater danger). The Enclave faction would be able to build bases inside of abandoned military ruins, and would be able to get resources from the ruins. Once the ruins are empty of resources, the base would remain, but would no longer add to their resource pool. The Brotherhood of Steel would be able to scavenge in a matter similar to that of the Wastelanders, but would have specific units to do so, which would be more effective at scavenging. The Super Mutant faction would get new units by taking prisoners from the other factions and bringing them to certain permanent bases to "convert" them. The only way to stop the unit flow is to destroy the bases. Certain types of units would be harder to capture, like "hero" units from the Wastelander faction, or high-level Brotherhood units, but converting these units would result in more powerful creations (captured heros can become Behemoths).
Leveling
While it wouldn't be a Fallout game without leveling, the system is different here. Only a few of the factions have "levelable" units. The Brotherhood combat units can be leveled up through battle experience, which would make them more powerful and versatile (certain available perks expand the functionality of the unit). The Brotherhood would level through perks, which would become available at a certain rank (Knight, Paladin, etc.). The Wastelander faction would level somewhat differently. As I stated before, all their units can scavenge from corpses and ruins. While combat experience would increase level, a level increase would not affect the unit much (it would unlock certain "privileges", like scavenging from more dangerous ruins, and a level up would increase unit strength a bit). Instead, it would give them the ability to use their loot from scavenging in different ways. The player could choose to use the loot to: a) Build more units at the buildings they control, or b) use the loot to upgrade the unit that found it. In other words, loot (like scavenged power armor or weapons) can be worn and used by the unit that found it (if it is the correct level), in order to improve the performance of the unit. If a tricked-out unit dies, only some of its items can be recovered, thus giving players an incentive to keep their men alive. The Enclave and Super Mutant factions would not level.
That's my thesis. Comment and tell me what you think, suggestions, comments, criticism, etc.