Below is a list of the modules I've chosen to include on my sites from their respective plugins. I've gone through each module and compared them to their counterparts, if they had one, and chose the ones that I believe either had the better feature set, more options, or better user experience, etc. Further down I've listed every module and my thoughts about each if you want more detail.
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Below is a list of every module offered by both plugins. I identify which plugin offers the module and when the module was first introduced (innovation leaders). Hover or click each list item to read my perspective on each module, specifically any special features or options that give one module version an edge over the other. Again I will try to keep this list as update as is reasonably possible.
Create beautiful 3D slider for your portfolio or gallery.
Create accordions with custom styling options.
Different source options like Posts or ACF
Add beautiful icons and images that are beautifully designed clickable elements to entice the users
Create beautiful and highly customizable menu
Powerful and flexible posts grid module with many options
A few more options
Break a content with Advanced Separators that can be just a line, line with icon, line with image or line with text
Icon background style
Preset and custom styling for creating beautiful Tabbed content for your Beaver Builder site.
More tab appearance options
One image trigger for full custom album/gallery
Animation option for navigation
Simple notification and alert boxes to grab user's attention
Display latest announcements, offers, discounts, or any notifications
Both plugins have their unique modules and settings so it'll be really hard to recommend one over the other. I can say there are some really nice quality of life things that UABB imploys like modules with hidden panels are shown when editing that specific content like with flip boxes. I also like that almost every module has a 'Doc' tab that links users to help articles about the module. These two items show how Brainstorm thinks about the end-user when creating their modules.
Share the knowledge! It helps me out too so thank you!