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Falls are the second leading cause of unintentional injury deaths worldwide. While numerous wearable fall detection devices incorporating AI models have been developed, none of them are used successfully in a fall detection application running on commodity-based smartwatches in real time. The system misses some falls, and generates an annoying amount of False Positives for practical use. We have investigated and experimented with an LSTM model for fall detection on a smartwatch. Even though the LSTM model has high accuracy during offline testing, the good performance of offline LSTM models cannot be translated to the equivalence of real-time performance. Transformers, on the other hand, can learn long-sequence data and patterns intrinsic to the data due to their self-attention mechanism. This paper compares three variants of LSTM and two variants of Transformer models for learning fall patterns. We trained all models using fall and activity data from three datasets, and the real-time testing of the model was performed using the SmartFall App. Our findings showed that in the offline training, the CNN-LSTM model was better than the Transformer model for all the datasets. However, the Transformer is a preferable choice for deployment in real-time fall detection applications.