Apples are the most important species in Polish fruit production, and their fresh fruit and processing products occupy a very important place in the European and world food economies. A natural process on the apple market is the replacement of older cultivars with new ones. Consequently, breeding work is being carried out all over the world to obtain new, attractive apple cultivars. In this work, four new apple hybrids obtained in the Department of Pomology and Horticulture Economics at the University of Life Sciences in Warsaw (WULS—SGGW), i.e., two red-skinned hybrids (‘I’P’ and ‘TL’) and two green-skinned hybrids (‘GL’ and ‘LG’), were tested for their main physico-chemical characteristics after harvest and after storage, as well as for their consumer acceptability in a comparison with three popular cultivars in Poland (‘Šampion’, ‘Golden Delicious’, and ‘Ligol’). The hybrids evaluated were differentiated in terms of the tested features. It was found that the fruits of the ‘GL’ hybrid had the highest firmness—both after harvest and post storage; it was also one of the highest-rated overall impressions by consumers among the cultivars tested (only ‘Ligol’ apples had higher scores). The hybrid with low fruit quality and low health-promoting properties at this stage of the study was ‘TL’, whose overall impression was also rated lowest by consumers. The study also showed that the content of bioactive compounds and antioxidant activity of apples can be higher in green-skinned cultivars compared to red-skinned cultivars.