Graphene is a unique material for the implementation of terahertz antennas due to extraordinary properties of the resulting devices, such as tunability and compactness. Existing graphene antennas are based on pure plasmonic structures, which are compact but show moderate to high losses. To achieve higher efficiency with low cost, one can apply the theory behind dielectric resonator antennas widely used in millimeter-wave systems. This paper presents the concept of hybridization of surface plasmon and dielectric wave modes. Then, via an analysis of one-dimensional structures, a comparison of the potential capabilities of pure and hybrid plasmonic antennas is performed from the perspectives of radiation efficiency, tunability, and miniaturization. Additionally, the impact of the quality of graphene upon the performance of the compared structures is evaluated. On the one hand, results show that hybrid structures deliver high gain with moderate miniaturization and tunability, rendering them suitable for applications requiring a delicate balance between the three aspects. On the other hand, pure plasmonic structures can provide higher miniaturization and tunability, yet with low efficiency, suggesting their use for application domains with high flexibility requirements or stringent physical constraints.