A building energy performance gap can be illustrated as the difference between the theoretical (methodologically defined) and the actual energy consumption. In EU countries, Energy Performance Certificates are issued when buildings are constructed, sold, or leased. This information is the first step in order to evaluate the energy performance of the building stock. In Serbia, when issuing an energy certificate, the adopted national methodology recognizes only energy consumption for heating. The main purpose of this paper is to evaluate the energy gap and estimate the relevance of an Energy Performance Certificate to meet the national energy efficiency or carbon target. An Energy Performance Certificate determines the theoretical residential and commercial building energy efficiency or its “design intent”. This research stresses the necessity of measuring and achieving reductions in actual energy consumption through system regulation and consumers’ self-awareness in buildings. The research compares the performance of the building stock (135) that is connected to the District Heating System (DHS), with its own integrated heat meter, to Individual Gas Boiler (IGB) systems (18), in the city of Novi Sad, Serbia, built after 2014. For the purpose of comparing energy consumption, 16 buildings were selected that are very similar in terms of design, operation, and location. The data used are derived from metered consumption data, official evidence of city service companies, and Energy Performance Certificates of the considered buildings. We have determined that IGB systems have a much wider specific annual performance gap (11.19–101 kWh/m²a) than the buildings in the DHS (3.16–18.58 kWh/m²a).