In your view, which structure of GDP (income or final expenditure) provides more reliable estimates of elasticities of GDP with respect to capital and labor in the aggregate production function by the equilibrium method?
I recon that both should give similar results (at least with respect to the measurement errors of those elasticities). If you get (significantly) different results than I would start looking for errors (in the data/method/implementation etc).
In a working paper of mine I employed five equilibrium approaches to estimating elasticities in Bulgaria’s aggregate production function. I had two objectives: first, to identify the best equilibrium approach to calculating elasticities in Bulgaria’s aggregate production function; and second, to measure quantitatively the contributions of capital, labor and total factor productivity to Bulgaria's economic growth under a currency board arrangement (CBA). An econometric procedure - ordinary least squares (OLS) estimation of Bulgaria’s aggregate production function - was used to determine the best equilibrium approach to calculating elasticities in this function. The OLS estimation demonstrated that the first equilibrium approach, which was based on the final expenditure structure of Bulgaria’s gross domestic product (GDP), provided the most reliable results of all five equilibrium approaches. The second objective of the research was accomplished by applying the growth accounting (GA) technique to Bulgaria for the period 1997-2013. The GA results implied that total factor productivity and capital stock were the main supply-side determinants of economic growth in Bulgaria under a CBA.
Theoretically, both of them should give similar result. In reality however, experience has shown that values from the expenditure approach gives a better result in equilibrium analysis.