Both of them deal with data of graph structure like a network community. Is there a big difference there?
Network analysis does not necessarily use deep learning techniques, while geometric deep learning (GDL) on graphs uses only deep learning techniques (that is, you train a neural network using gradient descent or other optimization methods). You can do some network analysis using GDL.
Both study properties of a network. The literature under respective titles seems to focus on certain topics.
Network analysis seems to focus on understanding the structure of a network. Centrality , modularity, assortativity etc are metrics used to study properties of networks. Key areas of research are for egs community detection, centrality measures, clustering algorithms, link prediction
GDL is oriented more towards using dataset structured as a graph as an input to machine learning problems like classification, regression. Key areas of research include graph representation, neural architecture.
Some problems like link prediction for example are present in both domains. Some problems like network construction for egs isn't covered deeply in both areas.
Some disciplines like algebraic graph theory appear in both disciplines. Fiedler vector for egs is studied in network analysis for community detection . Spectral analysis, matrix factorisation are ideas being explored in representation learning.