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
Display the Author Badge on the posts, pages in a stylish way
Different source options
Easily create great looking image comparison, before and after slider
More style options and slider options
Breadcrumbs Module allows you to create a hierarchical representation of the navigation links
Create a stylish business hours section that suits your website
A few more timing settings
Build trust and authority by fetching real reviews from Google and Yelp directly on to your website!
Create stylish call-to-action buttons
Variety of hover animations
Display Category or Custom Taxonomy on any page in a grid or carousel style
List and carousel options
Add a column separator between rows and columns
Create an attractive and simple Contact form for your website
Create magazine style layouts with any content type
More layout options
Allow your users to switch between two different content types
Use this module to create urgency on your site
Timezone and custom digit area shape
Use counters with icons and separators to show-off and attract users
Create attention-grabbing coupons anywhere on your website and display offers & discounts
Add a set of creative links that are both stylish and attractive with magical hover effects
Add device frames to your pages for beautifully showcasing your web designs or portfolio
Create beautiful one page websites
Create stylish dual button with various options
Nice divider option
Each button as style option
Increase user engagement on your site and get more followers with Facebook Modules
Create beautiful headings with built-in presets
Add creative, stylish headings to your website
Create, Organize & Display your FAQs with Schema Markup
Allow users to download a file using a File Download Button
Create a beautiful gallery with filters and overlay effects
Available in regular photo gallery module
Add dual side content on information boxes with flip animations.
Add a map to share a location. Keep it solo or pair it up with your contact info or an appealing form
Gravity Forms Module lets you take complete control of styling the forms
Button Style presets
Create heading with various styles, separators, and description. You can create dual color and dual font heading.
Separator and Icon styles
Create a colorful text box with hover affects
Show your content with style and hover effects.
Create & Display How-to Guides, Tutorials, and walk-throughs
Explore different styles to display a list with stunning icons as bullets to your list
Has a number list option
Get the best animation effects to display text when user hovers on an image.
With Image Hotspot module you can showcase product features, create virtual tours, and display information.
Drag and drop coordinate setup
Image Scroll module gives you a creative way to display Images on your website.
Create fancy adverts or information blocks with call to action
More image animation
Create beautiful content to showcase your products and services
Give your information a new look with icons and images on the circumference
Very unique at the moment
A very flexible and easy to use module to display content in vertical or horizontal list formats
Display Instagram photos from Instagram accounts
Use an Interactive banner with a beautiful animation effect and add text to explain the image further
Create WordPress Login forms easily
Social Login options
Create a grid or carousel to flaunt your client or partner logos
Create appealing call-to-actions that lets you add additional text with a fully customization button
Create custom popups with various trigger options - auto-load, on-click and exit intent
More content options
Exit intent trigger and close button controls
Display creative flyout panels in a responsive off-canvas panel
Make use of the Photo gallery module to display all your photos in a grid or masonry layout
Filterable by category options included
Overlay animations and thumbnail gallery
Showcase images in a beautiful layout
More images effects and on hover
Show your content in timeline style.
List your packages with various styling options
Dual pricing option
Create a menu for restaurants, cafes, bar, eateries or list any business services
Flaunt your progress or the development so far with advanced progress bars.
Multiple display options
Quick way to pull quotes
Add high definition images and logos on your WordPress website
Add glaring reviews to the site in beautiful designs
Beautifully designed Ribbons add to the beauty of your website.
Give seamless navigation power in your users hands with the Search Form module
Sitemap module allows you to create a sitemap page
Use slide boxes to slide out information when a user clicks or hovers on them
Display a list of your social media pages easily
Share your website content over different social media networks
More networks and styles
Rate content anywhere on your website
Add beautiful optin / subscribe forms that work with all popular mailing services
Create a table with custom data using various styling and sorting options
Advanced row and column options
A quick index at the top of the page/post can give an idea about topics explained within a post.
Useful for long posts
Show off your team of experts with this highly customizable module
Create testimonial slider and carousel with a few clicks
Icon or photo option
Tell your story with a beautiful timeline
Module to display your Twitter feed, Tweet buttons, Twitter embedded grid and timeline
Build customized user registration forms with additional fields and more styling options
More field and styling options
Video module allows you to integrate a video on your web pages with multiple styling options
Stick Video and YouTube subscription bar
More source options
Create beautiful video galleries with the highly optimized Video Gallery module
More platform specific options
Enhance your WooCommerce website with these three modules
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!