The D3 site needs to be updated to match the portraits on the other site. We are working on it.
I do have a question about the battletag changing however: The sc2 site should your user Sc2 character name (not battle tag) when posting while the D3 site uses your battletag. Is this not the behavior you're seeing?
I'm not sure if I'm answering this correctly or not, but it does the following:
On SC2 site it only gives the option to post using your character name for your SC2 profile.
On the D3 site it gives you the option of changing back and forth between SC2 profile and D3 profile. Using the D3 profile will show your profile name minus your battle tag. To get a person's D3 battletag you must either click the dropdown arrow by their name or view their profile. Clicking their profile will direct you to that person's D3 profile. When posting from a SC2 profile it also shows the profile, however, there is no displayed SC2 battletag. Clicking on the profile of someone posting on a SC2 account will redirect you to their account page on the SC2 side.
This can be frusterating at times because sometimes people ask for help on the D3 site, yet if they are posting from a SC2 account it is difficult to figure out how to see their D3 profile. The only way to currently do this is for them to either provide it, or it will be displayed if they edit their own posts.
I am also facing the OP's isdue. Hopefully you guys can address it soon.