As more deep learning models are being applied in real-world applications, there is a growing need for modeling and learning the representations of neural networks themselves. An effective representation can be used to predict target attributes of networks without the need for actual training and deployment procedures, facilitating efficient network design and deployment. Recently, inspired by the success of Transformer, some Transformer-based representation learning frameworks have been proposed and achieved promising performance in handling cell-structured models. However, graph neural network (GNN) based approaches still dominate the field of learning representation for the entire network. In this paper, we revisit the Transformer and compare it with GNN to analyze their different architectural characteristics. We then propose a modified Transformer-based universal neural network representation learning model NAR-Former V2. It can learn efficient representations from both cell-structured networks and entire networks. Specifically, we first take the network as a graph and design a straightforward tokenizer to encode the network into a sequence. Then, we incorporate the inductive representation learning capability of GNN into Transformer, enabling Transformer to generalize better when encountering unseen architecture. Additionally, we introduce a series of simple yet effective modifications to enhance the ability of the Transformer in learning representation from graph structures. In encoding entire networks and then predicting the latency, our proposed method surpasses the GNN-based method NNLP by a significant margin on the NNLQP dataset. Furthermore, regarding accuracy prediction on the cell-structured NASBench101 and NASBench201 datasets, our method achieves highly comparable performance to other state-of-the-art methods. The code is available at https://github.com/yuny220/NAR-Former-V2.