One of the principal goals of modern vehicle control systems is to ensure passenger safety during dangerous maneuvers. Their effectiveness relies on providing appropriate parameter inputs. Tire-road contact forces are among the most important because they provide helpful information that could be used to mitigate vehicle instabilities. Unfortunately, measuring these forces requires expensive instrumentation and is not suitable for commercial vehicles. Thus, accurately estimating them is a crucial task. In this work, two estimation approaches are compared, an observer method and a neural network learning technique. Both predict the lateral and longitudinal tire-road contact forces. The observer approach takes into account system nonlinearities and estimates the stochastic states by using an extended Kalman filter technique to perform data fusion based on the popular bicycle model. On the other hand, artificial neural networks (ANN) were trained and tested using experimental data to estimate contact forces. These were built with a single hidden layer. Furthermore, the ANN input parameters were carefully selected to ensure appropriate convergence and avoid overtraining. All predictions from both approaches are validated against experimental data. Results show that the observer approach is capable of predicting forces with higher accuracy as consequence of the detailed vehicle dynamic models introduced on the overall estimation scheme. The ANN approach is limited to the specific car from which the training data was collected and is purely based on machine learning. Nevertheless, it provides a fast and straightforward alternative to obtain force estimates with comparable accuracy to observer approaches.