[kevsim]

Go to Preferences->Profiles->Default and find the option over on the right for "Working Directory". Then set it to "Reuse previous session's directory".

Then for me Cmd+D and Cmd+Shift+D (split with current profile) gives the same current directory.

[sorahn]

Depending on your workflow, you might even want the advanced configuration version of this.

I want new windows (which I rarely use) and new tabs to be my home directory, but split panes to be the directory I was in when I split. Works wonders.