As gabriel said, functionality wise they are the same. As a user you should see no difference.
The big advantage is that the store version gets updated automatically. New versions are available only a few days after we have announced the release, as any new release needs to be approved by Microsoft, but I don’t see this as a big issue.
One downside is if course that it is a Microsoft controlled store. You should be aware that Microsoft knows what you install there and how often and when you use the apps.
So if you find the Store install more convenient, and you don’t mind using you MS account for software installs, you can use the store version.
There is a technical downside to the store version, but that is mostly an issue from a development point of view: It is harder to debug. Especially if there is a bug that prevents it to start at all it is difficult to figure out the cause. In such situations I would ask users to install Picard using the installer. Luckily so far this was not much of a problem in practice.