Where one can see the world economy sectors comparison by value? I'd like to know which economy sectors in the world are the biggest. Does such statistics exist? If so, how accurate and up to date is it? If not, what can be used instead?
The United Nations Industrial Development Organization (UNIDO) maintains a variety of databases comprising statistics of overall industrial growth, detailed data on business structure and statistics on major indicators of industrial performance by country in the historical time series. The UNIDO publishes the Industrial  Development  Report  2016 and offers some statistics. 

This is one of the most reliable source of industrial data although data are still incomplete for some developing countries.

Broad Sectors: world value added over time. (Source: UNIDO)


Within Manufacturing: In  2013,  the  dominant  global  manufacturing  indus-tries were food and beverages (12.0 percent), chemicals and chemical products (11.7 percent) and machinery and equipment (8.5 percent; Table 7.2) (source: UNIDO's Industrial  Development  Report  2016)