Generative graph self-supervised learning (SSL) aims to learn node representations by reconstructing the input graph data. However, most existing methods focus on unsupervised learning tasks only and very few work has shown its superiority over the state-of-the-art graph contrastive learning (GCL) models, especially on the classification task. While a very recent model has been proposed to bridge the gap, its performance on unsupervised learning tasks is still unknown. In this paper, to comprehensively enhance the performance of generative graph SSL against other GCL models on both unsupervised and supervised learning tasks, we propose the SeeGera model, which is based on the family of self-supervised variational graph auto-encoder (VGAE). Specifically, SeeGera adopts the semi-implicit variational inference framework, a hierarchical variational framework, and mainly focuses on feature reconstruction and structure/feature masking. On the one hand, SeeGera co-embeds both nodes and features in the encoder and reconstructs both links and features in the decoder. Since feature embeddings contain rich semantic information on features, they can be combined with node embeddings to provide fine-grained knowledge for feature reconstruction. On the other hand, SeeGera adds an additional layer for structure/feature masking to the hierarchical variational framework, which boosts the model generalizability. We conduct extensive experiments comparing SeeGera with 9 other state-of-the-art competitors. Our results show that SeeGera can compare favorably against other state-of-the-art GCL methods in a variety of unsupervised and supervised learning tasks.