Cross-Platform User Identification (CPUI) aims to identify social media accounts belonging to the same real-world user across different platforms. This task is vital for combating cybercrime, where malicious users create multiple accounts, and for enhancing user modeling in fields such as sociology, economics, and epidemiology. Prior research suggests that vector-based encoding of a local network graph may fall short when faced with real-world inconsistencies such as platform dependency and data sparsity. In response, variational encoding, which models the data as normal distributions explicitly, has been proposed as a more robust alternative. In this paper we present a comparative study of vector and variational encoding approaches in the context of a binary CPUI classification task. For this goal, we constructed a synthetic heterogeneous graph derived from 277 research papers authored within an engineering department. Using vector-embedding of the textual context of the papers as features, various models were trained to evaluate the advantage of variational encoding in CPUI. Experimental results show that the standard vector encoding consistently outperforms the variational models in terms of accuracy, F1-score, and AUC-ROC. While all models achieved high performance (accuracy around 90%), there was no empirical advantage to using variational encoding in our experiments. These findings suggest that the benefits of variational encoding may depend on the presence of real-world data inconsistencies that our synthetic dataset lacks.