First, you misread my comment.
I was presuming both sides were armed with the same weapons unless they're clearly overkill.
Second, I was ignoring fortification and other defense modifiers, and presuming any shot would hit. Which is a fair enough assumption when both sides have the same modifiers. It would tend statistically towards this result after all.
Third, combat rounds occur at the same time for all players. Otherwise the first to go has the advantage.
Fourth, your cost equal example is the only example that favours the unarmoured infantry. Equal Size with the same weapons? Armoured infantry. Equal numbers? Armoured infantry or draw.
The whole point of the debate is "if we go by cost instead of size". Yes, heavy armor gives a bonus for no increase in size, so of course any simulation of equal size the heavy armor is going to win or at worst tie. That goes unsaid.
Second, you're wrong that the same weapons favors armored infantry. Your example is "same weapons tie" but only if you define the "same weapons" as exclusively weapons that are good against unarmored infantry but not armored infantry.
Same cost, same weapons, and those weapons are personal or crew served anti-personnel (Anything with base AP of 10 or less, basically)? A tie.
Same cost, same weapons, and those weapons are heavy crew served anti-personnel? Unarmored infantry will
destroy the armored infantry, because the armor doesn't matter against the weapon and there are twice as many.
Same cost, same weapons, and those weapons are anti-vehicle? Anti-vehicle isn't great against infantry, but both sides are using them and they're as good against the armored infantry as unarmored. Unarmored infantry will again mop the floor with the armored, because the armor doesn't matter and there are twice as many.
Same cost, same weapons, and both sides are using the same mix of weapons? Unarmored infantry will also win, because they literally tied when both sides used the ideal weapons against unarmored infantry and any mix has to be worse against them and will likely be better against the armored infantry.