Physical activity has a strong influence on mental and physical health and is essential in healthy ageing and wellbeing for the ever-growing elderly population. Wearable sensors can provide a reliable and economical measure of activities of daily living (ADLs) by capturing movements through, e.g., accelerometers and gyroscopes. This study explores the potential of using classical machine learning and deep learning approaches to classify the most common ADLs: walking, sitting, standing, and lying. We validate the results on the ADAPT dataset, the most detailed dataset to date of inertial sensor data, synchronised with high frame-rate video labelled data recorded in a free-living environment from older adults living independently. The findings suggest that both approaches can accurately classify ADLs, showing high potential in profiling ADL patterns of the elderly population in free-living conditions. In particular, both long short-term memory (LSTM) networks and Support Vector Machines combined with ReliefF feature selection performed equally well, achieving around 97% F-score in profiling ADLs.