The estimation of human mobility patterns is essential for many components of developed societies, including the planning and management of urbanization, pollution, and disease spread. One important type of mobility estimator is the next-place predictors, which use previous mobility observations to anticipate an individual’s subsequent location. So far, such predictors have not yet made use of the latest advancements in artificial intelligence methods, such as General Purpose Transformers (GPT) and Graph Convolutional Networks (GCNs), which have already achieved outstanding results in image analysis and natural language processing. This study explores the use of GPT- and GCN-based models for next-place prediction. We developed the models based on more general time series forecasting architectures and evaluated them using two sparse datasets (based on check-ins) and one dense dataset (based on continuous GPS data). The experiments showed that GPT-based models slightly outperformed the GCN-based models with a difference in accuracy of 1.0 to 3.2 percentage points (p.p.). Furthermore, Flashback-LSTM—a state-of-the-art model specifically designed for next-place prediction on sparse datasets—slightly outperformed the GPT-based and GCN-based models on the sparse datasets (1.0 to 3.5 p.p. difference in accuracy). However, all three approaches performed similarly on the dense dataset. Given that future use cases will likely involve dense datasets provided by GPS-enabled, always-connected devices (e.g., smartphones), the slight advantage of Flashback on the sparse datasets may become increasingly irrelevant. Given that the performance of the relatively unexplored GPT- and GCN-based solutions was on par with state-of-the-art mobility prediction models, we see a significant potential for them to soon surpass today’s state-of-the-art approaches.