I have not trialed the most recent version of AuroraHDR or whatever it is being called now, but the first two or three iterations were not very good at coping with true HDR scenes. The tone mapping operators in particular produced terrible results that were not undoable with the set of controls in the interface. There were several issues I had with the tone, color and rendering of transitions, particularly at edges with fine detail or edges that were out of focus due to bokeh effects. Maybe this has changed with the most recent iteration. You will notice from the marketing materials that most images that are show as examples come from a sequence of three JPEGs or something similar. This is probably a sign that the scene tonal range that Aurora can accept as a typical working range is not super big.
HDR Express is a slimmed-down version of HDR Expose and can cope with a wide dynamic range, typically. If I had to suggest one application over the other, I would suggest HDR Express. I use HDR Expose, but I am assuming that HDR Express still shares the basic merge and tone mapping controls with HDR Expose.
Give both of them a try with a few sets of HDR data that test various features and weak points of HDR applications. Then you can compare apples to apples in terms of ease of use, quality of merger and color and tone reproduction of the LDR output.