I need some more use case drill down of use case for each. Specifically I need clarification on
a. Is asset share implementation lead to an external facing (public facing) portal where internal organization can collaborate with external partners? Or it is meant to be just showing assets to external users
b. If my sole purpose is to collaborate with external partners in a secure environment, should I go with Brand portal
Asset Share documentation does not articulate clearly the use case...all it reads is "it's a reference implementation of asset share -like functionality". Does not go into - is it for outside users, how will users authenticate, what data source ? or it is essentially sharing your assets as a public repository where consumers can share anonymously?
You can use Asset share portal for sharing assets securely and anonymously with external partners or users who are not AEM users. The asset share is a regular AEM site and you can integrate with any authentication provider as per your needs. Since asset share is open source reference implementation, you have full control on how to present the information and add or modify existing features. It is a fully customizable solution and you need to maintain it yourself just like any other bespoke solution.
The brand portal is similar to asset share but it is Adobe managed offering on the cloud. So it does not give you the flexibility to customize extensively or make any changes to the integration with AEM. If I am not wrong you can just do small tweaks of adding custom branding like logos, and changing headers etc. So you should assess all the capabilities and features of brand portal before you go for it.
You can refer this article https://hoodoo.digital/blog/brand-portal-vs-asset-share-commons to know more about the offerings of asset share commons and brand portal. Both Brand Portal and Asset Share Commons seem to basically do the same thing, provide assets stored in your AEM Assets to users without allowing them access to items that should be protected. Both options are meant to be simple in setup so that the implementations are minimal.
This asset share commons is an open-source project, see  for more details. If you want to have a good jumping-off point rather than starting from scratch to build your own tool, this is an excellent resource.