IAF vs PAF: War of doctrines and the question of aircraft downings

Now that both the IAF and PAF have made their formal claims of having shot down the other's aircraft in the 87-hour, predominantly aerial conflagration in May, we can ask a larger question

I can begin this with a trick question: If in a war, one side lost 13 aircraft to combat and the other five, who won? All of the active India-Pakistan wars and conflicts have been short, 22 days in 1965 being the longest. Operation Sindoor was just over three days. Whenever a conclusive outcome like a capitulation and mass surrender is missing, there’s scope for both sides to claim victory. 

There is clarity in some situations, however. We Indians believe we won every war or skirmish, but accept that we lost 1962 to China. Similarly, the Pakistanis concede defeat in