I know I might be a biased voice, but I use Tableau Mobile to connect back to Tableau's own internal Servers to check up on my daily dashboards for my day to day work. To clarify - Tableau Mobile is really just an app interface for Tableau Server or Tableau Online; content is still managed in those platforms and users still need license to access that platform. I really don't particularly see any cons since the users don't need to give up their regular browser access to these platforms if they choose to use Tableau Mobile; it simply acts as another entry point back to my Tableau Server that's more native to mobile device platform.
As for pro's, there's a lot:
- Interface is easier to track back to my favorite visualizations
- It does a great job of identifying the device type to take advantage of touch enhanced capabilities and Device-Specific Dashboard Designs
- Offline Snapshots are invaluable as I travel, since it still allows me to review the dashboards since they were last updated when I have connectivity back to the Tableau Server. This is very specific functionality to Tableau Mobile apps
There are some functionality that are on the browsers that have not made its way into the App as well - things like comment options at the bottom each viz. Over time though, these features will likely find its way into Mobile Apps as well.
Of course, each organization have their unique concerns and visions with mobiles devices: how to enable access for these devices to communicate with Tableau Server/Online, how they want to approach dashboard design if multiple platforms are used, branding on the app, etc. I would check out the Tableau Mobile Deployment Guide and try to have these discussions. A lot of the Tableau Mobile development has focused on making it easier for organizations to adopt a mobile strategy for Tableau, including integrations with Mobile Device Management tools such as Airwatch/MobileIron. That said, if you can get acceptance to leverage Tableau Mobile to connect back to Tableau Server/Online, it will be worth it and will streamline the experience on mobile devices.