Well, frankly, I have no idea what die rolls go on behind the scenes in any Arms Race game on these forums. The design and revision rolls make sense, but as to how victory is decided, I have no idea. Every attempt at designing my own behind-the-scenes system so far, however, has resulted in an overly complicated mess with not much flexibility.
Sensei's actually posted a system on how he does it. Basically, he has a set of categories and whatever side has a bigger advantage due to quality and cost of their designs in that area gets a point, with ties awarding no points. Whichever has the most points wins in the area. The system is somehow weighted based on what the category is as well as terrain and we don't know how that precisely works, but that's the barebones of it.
Given this, we could possibly make a spreadsheet to give values for categories to make what amounts to an Arms Race battle determination grid. First column would be a list of labels defining categories and subsequent columns being different biomes with data determining what each category's weight in that biome would be. To keep things balanced, all of the weights could total up to a specific number.
Example for that last bit: For Plains, Hills, and Mountains, Rifles could have a weight of 1 in each for a total of 3, and Tanks could have a weight of 1.5 in Plains, 1 in Hills, and .5 in Mountains also resulting in a total of 3.
This would admittedly result in a bit of min-maxing, but that is kinda done in reality since people do want to get the most effect in an area...
Edit: One thing I can admit is that players and GMs could come up with things that wouldn't fit into existing categories, but if we steadily expand we will get more and more of these unforeseen slots covered.
Edit 2: Probably want to divide between pre and post gunpowder (far future can kinda get bundled up into this latter. Just need to rename the biomes to planet types, and sea to space, and you can get a rough fit). They could intermix, but the latter kinda drastically overturned how warfare is waged. Magic is kinda a difficult fit, but what can't fit into one of the existing categories if you squint (ex. Magic Carpets could considered to work along the lines of aircraft) can be made to have their own section (ex. Summoning).