There are other metrics, but I think you will be bit disappointed because they are not broader but rather narrower in scope.
A good overview of various metrics used can be found in this Plummer et al 2010 paper from Asian Development Bank (which by the way has a lot of very informative documents on various topics despite you hardly ever hear about it). Some non-exclusive list of measures of benefits from trade:
- using the Viner 1950 model to measure magnitude of trade creation ( when FTA leads to inefficient
home production is replaced with efficient imports from an FTA partner) is larger (smaller) than trade
diversion (FTA leads to efficient imports from the rest of the world
with inefficient imports from an FTA partner).
- examining trade volumes and terms of trade.
- estimation of consumer & producer surplus from prices and estimated demand and supply function.
Measures of increase in welfare, perhaps?
Problem is that we do not have generally accepted measure of welfare. Utility can't be measured on aggregate level, there are no direct time series data on consumer & producer surplus and even estimating that at a point in time is pain, indexes like Human Development Index (Trabold-Nübler 1991) and similar things can be very subjective (in deciding weights of various items etc). GDP, albeit flawed is still the measure to go for most researchers mainly because it is considered more objective and data are readily available.
It occurs to me that the standard economic argument for free trade in terms of comparative advantage goes back to Ricardo in the early 19th century, while the concept of GDP was only developed in the 20th century.
Actually, real GDP, despite being invented in 20th century, can be used to measure benefit of trade in Ricardian model.
In Ricardian model trade is beneficial because it allows society to expand production possibility frontier. That is with free trade in Ricardian model a country is able to enjoy more goods at lower prices. Real GDP increases when production increases or when aggregate prices drop. Hence, if you want to test Ricardian model real GDP is completely fine.
In fact, I even recall that during my MSc in international trade class when we were building modern versions of Ricardian or Heckscher-Ohlin models in Matlab, we were even withing purely numerical modeling constructing GDP by summing output at market prices in the model and compared effects of trade by looking what happens to GDP. We were also contrasting this to results when you use utility and the results generally matched although that might have been consequence of representative agent assumptions and might not translate into heterogenous agents setting. However, Ricardo himself did not had some model of utility maximizing agents. He only looked at how much goods and services people can enjoy and at what prices.