This study compared the effects of seed treatment with low-pressure cold plasma (CP) and atmospheric dielectric barrier discharge (DBD) plasma on morpho-biochemical traits in Stevia rabaudiana Bertoni plants cultivated by two methods: in soil and aeroponics. We investigated the impact of the treatments on the germination, plant growth, and content of secondary metabolites, namely steviol glycosides (SGs), rebaudioside A (RebA), and stevioside (Stev), as well as phenolic compounds and flavonoids. Seeds were treated for 2, 5, and 7 min with CP or DBD and 5 min with vacuum six days before sowing. All growth parameters in aeroponics exceeded the parameters of seedlings in the corresponding groups cultivated in soil. Seed treatments stimulated SGs biosynthesis in seedlings grown in soil, except for CP7. Although there were no stimulating effects of seed treatments on SGs in aeroponics, overall SG concentrations were considerably higher compared to plants cultivated in soil: the RebA+Stev concentration was 1.8–2-fold higher in the control, V5-, and CP-treated groups, and 1.3-fold higher in the DBD5 and DBD7 groups. Thus, aeroponic cultivation has the potential to improve the growth and synthesis of SGs in stevia, while a combination of aeroponics with seed treatments only increases the content of antioxidants and antioxidant activity.