Nominal GDP versus PPP in comparing military spending of different countries? Military spending as percentage of GDP is the most used measure of the economic capability of a certain country/military. But Some countries like India for example, have a huge difference between their nominal and PPP GDP (2 billion vs 7.7 billion). So which number is more meaningful to express the economic capability of a certain military ?
One argument for using the exchange rate:


  Market exchange rates are determined by the supply and demand of
  currencies used in international transactions. However, the prices of
  many goods and services on domestic markets are determined in partial
  or complete isolation from the rest of the world. Therefore, the MERs
  do not always accurately reflect differences in price levels between
  countries.
  
  An alternative is to use purchasing power parity (PPP) conversion
  factors (or PPP exchange rates). The PPP dollar rate of a country's
  currency is defined by the World Bank as 'the number of units of a
  country's currency required to buy the same amount of goods and
  services in the domestic market as a U.S. dollar would buy in the
  United States'. >1  The only PPP rates available for all countries are
  GDP- based basket of goods and services that are major components of
  the gross domestic product. Such GDP-based PPP rates are designed to
  control for differences in price levels and thus to provide a measure
  of the real purchasing power of the GDP of each country.
  
  Using GDP-based PPP rates instead of MERs for currency conversion
  results in much higher output and expenditure figures for many
  developing and transition countries since they have relatively low
  prices for non-traded goods and services—thus giving the currency
  higher purchasing power. A unit of local currency therefore has
  greater purchasing power within a developing country (which is better
  reflected by using PPP rates) than it has internationally (which is
  what is reflected by using MERs). For those such developing and
  transition countries for whom data was available for 2008, the median
  increase in military expenditure figures from using PPP rates instead
  of MERs was around a factor of 2. Three-quarters of these countries
  would see their relative figures increase by at least two-thirds.
  Meanwhile, using PPP rates would cause the GDP and military
  expenditure figures of most 'developed' countries to fall relative to
  the USA, by a median rate of 17 per cent—reflecting the low value of
  the US dollar at market exchange rates in 2008. However, the
  reliability of such PPP rates is lower than for MERs, since PPP rates
  are statistical estimates, calculated on the basis of collected price
  data for a basket of goods and services for benchmark years. Between
  benchmark years, the PPP rates are extrapolated forward using ratios
  of prices indexes, either GDP deflators or consumer price indexes.
  Like all statistical estimates they are subject to a margin of error.
  
  Furthermore, GDP-based PPP rates are of limited relevance for the
  conversion of military expenditure data into US dollars. Such PPP
  rates are designed to reflect the purchasing power for goods and
  services that are representative of spending patterns in each country,
  that is, primarily for civilian goods and services. Military
  expenditure is used to purchase a number of goods and services which
  are not typical of national consumption patterns. For example, the
  price of conscripts can be assumed to be lower than the price of a
  typical basket of goods and services, while the prices of advanced
  weapon systems and of their maintenance and repair services can be
  assumed to be much higher. The extent to which this data reflects the
  amount of military goods and services that the military budget can buy
  is not known. Due to these uncertainties, SIPRI uses market exchange
  rates to convert military expenditure data into US dollars, despite
  their limitations.


Stockholm International Peace Research Institute: Monitoring Military Expenditures  

But wages are a big part of military costs and those are not paid with PPP GDP but rather domestic GDP. MEASURING HARD POWER: CHINA’S ECONOMIC GROWTH AND MILITARY CAPACITY says that both methods have merits but at least in China, both methods understate military capacity. 


  The most appropriate way to compare real military capacity across
  countries is to deflate each country’s actual, or potential, military
  spending by the price of real military services in each country.
  Unfortunately military price indices do not exist for most countries.
  The aim of this paper, therefore, is to develop a simple method for
  computing a relative military price index, that deflates nominal
  spending into units of real military services, using readily
  accessible data. The ratio of two countries’ military price indices
  then gives an exchange rate that provides an index of relative real
  military capacity across countries. We use this military exchange rate
  to compare the level and growth of China’s real military capacity
  relative to the USA. 4 We obtain two key results. First we find that
  the value of the RMB, in terms of its ability to purchase real
  military services, is greater than both its market exchange rate value
  and its PPP value. This suggests that conventional estimates of GDP
  understate China’s real military capacity, but also that PPP exchange
  rate comparisons are much closer to the actual value than market
  exchange rate comparisons. This is mainly because of the very low cost
  of labor in China relative to the USA. 
  ... 
  
  If we wish to infer
  country’s miliary capacity based on the size of its economy, however,
  standard PPP indices also pose a problem insofar as they reflect the
  relative price of an average basket of goods produced in the economy
  and this average price index may differ substantially from the price
  of military services. Thus Crane et al (2005) argue that, while
  military services have large personnel costs, a substantial share of
  military equipment purchased by developing-country militaries is
  imported or incorporates com- ponents that are manufactured from
  materials and parts sold at world market prices, such as electronics,
  diesel engines, or aircraft frames. Thus they suggest that, for some
  purposes, GDP measured at market exchange rates may give a more
  realistic picture of changes in military capacity (Crane et al 2005,
  pp.16-17). Similarly, the two principle military statistical
  abstracts, The Military Balance published by The International
  Institute for Strategic Studies (IISS), and the Stockholm Interna-
  tional Peace Research Institute’s (SIPRI) Yearbook report relative
  military spending and relative GDP in terms of $US converted at market
  exchange rates and also at PPP ex- change rates. IISS (2012) notes
  that market exchange rates are likely to understate the true level of
  economic resources allocated towards defence since food material and
  hous- ing costs will be lower in China, but remain noncommittal in
  recommending a preferred price index. 8 Thus they often report a
  weighted average of PPP and market exchange rates when discussing
  China’s real military capacity relative to the USA.