Artificial intelligence can detect suicidal ideation manifestations in texts. Studies demonstrate that BERT-based models achieve better performance in text classification problems. Large language models (LLMs) answer free-text queries without being specifically trained. This work aims to compare the performance of three variations of BERT models and LLMs (Google Bard, Microsoft Bing/GPT-4, and OpenAI ChatGPT-3.5) for identifying suicidal ideation from nonclinical texts written in Brazilian Portuguese. A dataset labeled by psychologists consisted of 2,691 sentences without suicidal ideation and 1,097 with suicidal ideation, of which 100 sentences were selected for testing. We applied data preprocessing techniques, hyperparameter optimization, and hold-out cross-validation for training and testing BERT models. When evaluating LLMs, we used zero-shot prompting engineering. Each test sentence was labeled if it contained suicidal ideation, according to the chatbot's response. Bing/GPT-4 achieved the best performance, with 98% across all metrics. Fine-tuned BERT models outperformed the other LLMs: BERTimbau-Large performed the best with a 96% accuracy, followed by BERTimbau-Base with 94%, and BERT-Multilingual with 87%. Bard performed the worst with 62% accuracy, whereas ChatGPT-3.5 achieved 81%. The high recall capacity of the models suggests a low misclassification rate of at-risk patients, which is crucial to prevent missed interventions by professionals. However, despite their potential in supporting suicidal ideation detection, these models have not been validated in a patient monitoring clinical setting. Therefore, caution is advised when using the evaluated models as tools to assist healthcare professionals in detecting suicidal ideation.