Uncertainties in estimates of Equilibrium Climate Sensitivity (ECS) and Transient Climate Response (TCR) are influenced by observational datasets. Variability exists not just among the data products, but also within the creation of individual ones. This includes significant variations among ensemble members within a single data product. Using the optimal fingerprint approach combined with Bayesian updating, we quantify the uncertainties in ECS and TCR estimates arising from both individual datasets and their various groupings. Our methodology, utilizing both spatial and temporal data, reveals impacts on the estimates of ECS and TCR. As we assess different groupings of observational data products, we observe that using products sharing identical Sea Surface Temperatures (SST) introduces a discernible biases. Furthermore, these results highlight that the variations among ensemble members within a single data product are as influential as the disparities across multiple data products.