Accurate detection of change points (CPs) and turning points (TPs) in Interferometric Synthetic Aperture Radar (InSAR) time series (TS InSAR) is critical for reliable geohazard monitoring and early warning systems. We introduce a standardized comparison to rigorously evaluate seven CP/TP detectors, encompassing four novel deep learning architectures (MLP, MALkCNN, ATGLSTM, CNN-LSTM), two established deep learning baselines (LSTM+TGLSTM, BiLSTM+U-Net), and a fast statistical detector (STPD). Our comprehensive evaluation spans 100,000 synthetic time series and real Sentinel 1 data stacks from diverse European geohazard sites (Italy, Germany, Iceland), quantifying performance through accuracy metrics (precision, recall, F1-score), change magnitude error (RMSE, mm·yr⁻¹), agreement with co-located GNSS stations (r), and computational throughput. Among the tested models, ATGLSTM demonstrates superior detection accuracy (F1 up to 0.93 on synthetic and 0.80 on real data), exhibiting remarkable robustness to speckle noise and temporal gaps due to its attention and time gating mechanisms. While CNN-LSTM yields the strongest agreement with GNSS measurements (r≈0.88), the STPD method provides unparalleled efficiency (~0.2 s per 1,000 series), confirming a distinct accuracy–efficiency trade off. Based on these findings, we propose a hybrid operational pipeline that leverages STPD for rapid, large scale screening and ATGLSTM for high precision refinement of flagged candidates. This two stage approach preserves optimal detection accuracy while substantially reducing computational cost, offering a scalable solution for operational TS InSAR monitoring. Our comparison, datasets, and code are made publicly available to catalyze future research and the development of robust, operational pipelines and multi sensor fusion frameworks.