So now I've had the chance to test this out a bit further and it looks like there is a difference between users who have been added to the Azure AD of the tenant and those who haven't. If you have been added, it just shows you the login box immediately when you click the sharing link. I suspect that those of my colleagues who are sharing with external partners would not be able to explain what is going on to those partners. It would be really helpful if the first thing they saw was a page which said something along the lines of "you are trying to access some content shared with you from OneDrive and for that you have to sign in with a Microsoft Account..." or something to that tune.
Secondly, if I'm sharing with an external user who hasn't been added to AAD, he or she will be sent a code, even if they are already logged in to their Microsoft Account, which to me seems a bit confusing.
Thirdly, once they do get get access, there is a difference between what I can do as a user who's registered in AAD versus one who isn't. As I've previously stated, we'd really like to have all the same features available as if we were sharing with an internal user.
Thank you!