PPP is for comparing consumer lifestyles. World-tradeable goods like military hardware are precisely the kind of situation where PPP adjustments should not be made.
Of course the sums are not directly comparable for other reasons, such as corruption in Russia and procurement dysfunction in the US. But those factors would need to be estimated explicitly.
(EDIT: Thanks for the replies, I hadn't heard that there also exist specific estimates of "defense-sector PPP", so I acknowledge what I wrote above was wrong.)
Is the “world-tradeable” aspect so relevant? Nuclear warheads are going to be locally built and would be send in missiles that would also be built in Russia. The PPP argument is that it’s much cheaper to pay a bunch of rocket engineers and nuclear scientists in Russia, in rubles than in Los Alamos, in dollars. Same for all the logistics chain from raw materials to final assembly, upkeep, and maintenance. If your steel is dirt cheap because you’re full of ore and gas is plentiful, and your workers are paid peanuts, then your tanks are going to be cheap, at least for your own use, regardless of how much they cost in another country. So why would PPP be irrelevant in the case of military hardware?
A russian soldier is paid less than an American. A russian factory worker making military equipment is paid less than their American counterpart, leading to lower cost of that equipment. I don't see a problem describing that difference as ppp.
What a soldier or worker is paid only matters in a vacuum, you have to consider the pipeline from military budget to the actual good or service. That includes both commodities bought on the world market (E.G. steel) and corruption raising costs for the same good (which is a problem for both the US's military-industrial complex and Russia's oligarchy).
That being said though when the budgets are off by an order of magnitude there's no way to make that back just via lowering wages a bit
What's the cost of commodities in building a tank? Yeah fine both an Abrams and a t90 have a few tonnes of steel in it. That doesn't account for a fraction of the final cost though.
Maintenance requires labour. Labour has different prices in different countries. You can compare that labour cost.
Of course the sums are not directly comparable for other reasons, such as corruption in Russia and procurement dysfunction in the US. But those factors would need to be estimated explicitly.
(EDIT: Thanks for the replies, I hadn't heard that there also exist specific estimates of "defense-sector PPP", so I acknowledge what I wrote above was wrong.)