Volatile and non-volatile chemical profiles, free and total SO2 and dissolved oxygen content were studied in three red (Merlot, Lagrein red, St. Magdalener) and one rosé (Lagrein rosé) wine after 30 months of storage in bottles. Each wine was sealed with closures made of a ‘blend’ (B) of natural cork microgranules and polymers without glue and was compared with wines closed with other types of corks (C; a technical cork 1 + 1, or an agglomerated natural cork or a natural one-piece cork). Glutathionyl caftaric acid (GRP) was inversely correlated with total SO2 content and was higher in all three red wines closed with B compared to C, whereas epicatechin was higher in three wines closed with C compared to B. Three volatile compounds formed by fermentation (ethyl butanoate, isoamyl lactate, and octanol) were inversely correlated with both free and total SO2. In terms of their volatile profiles, ethyl octanoate and 2,3-butanediol were significantly higher in the Lagrein red wines closed with C closures, whereas no significant difference was observed in Merlot, Lagrein rosé and St. Magdalener wines. Small differences in some phenolic compounds due to the type of closure were found: GRP, syringic acid, (+)-catechin, and (−)-epicatechin differentiated the Merlot wines closed with B from the C closures. Protocatechuic acid and GRP levels differentiated the Lagrein red wines according to their closure type, whereas only (−)-epicatechin differentiated the Lagrein rosé wines. GRP, caffeic acid, (−)-epicatechin, and anthocyanin content differentiated the St. Magdalener wines according to their closure type. Even though St. Magdalener and Lagrein rosé closed with C could be distinguished from those closed with B by using the (sensory) triangle test (α = 0.05), these differences appeared to be relative as it did not include all the wines in a systematic manner.