Strawberry cultivars Portola and Enduro, as well as raspberry cultivars Enrosadira and Kwazi, were evaluated for their antioxidant potential after treatment with gaseous ozone and different refrigeration storage conditions. Their antioxidant capacity was investigated with ABTS and DPPH methods, and the chemical composition was determined by measuring the total phenolic (TPC) and flavonoid (TFC) compounds. The classification of different samples of berry puree was influenced significantly by both the cultivars and the refrigeration storage method. Moreover, FTIR spectroscopy coupled with chemometrics was used as an alternative technique to conventional methods to determine the chemical composition of strawberries and raspberries. The chemometric discrimination of samples was achieved using principal component analysis (PCA), hierarchical clustering analysis (HCA) and linear discriminant analysis (LDA) modelling procedures performed on the FTIR preprocessed spectral data for the fingerprint region (1800–500 cm−1). The fingerprint range between 1500 and 500 cm−1, corresponding to deformation vibrations from polysaccharides, pectin and organic acid content, had a significant impact on the grouping of samples. The results obtained by PCA-LDA scores revealed a clear separation between four classes of samples and demonstrated a high overall classification rate of 97.5% in differentiating between the raspberry and strawberry cultivars.