There has been a growing interest in developing image super-resolution (SR) algorithms that convert low-resolution (LR) to higher resolution images, but automatically evaluating the visual quality of super-resolved images remains a challenging problem. Here we look at the problem of SR image quality assessment (SR IQA) in a two-dimensional (2D) space of deterministic fidelity (DF) versus statistical fidelity (SF). This allows us to better understand the advantages and disadvantages of existing SR algorithms, which produce images at different clusters in the 2D space of (DF, SF). Specifically, we observe an interesting trend from more traditional SR algorithms that are typically inclined to optimize for DF while losing SF, to more recent generative adversarial network (GAN) based approaches that by contrast exhibit strong advantages in achieving high SF but sometimes appear weak at maintaining DF. Furthermore, we propose an uncertainty weighting scheme based on content-dependent sharpness and texture assessment that merges the two fidelity measures into an overall quality prediction named the Super Resolution Image Fidelity (SRIF) index, which demonstrates superior performance against state-of-the-art IQA models when tested on subject-rated datasets.