They are both directory servers, even both ones with an LDAP protocol interface, but with a different focus.
While providing seemingly the same goal of single-sign-on and identity management, Active Directory is clearly focused on Windows servers and clients and Windows services within trusted domains. Its primary purpose is user authentication/authorization and management of servers, services and hosts within the relatively narrow scope of Microsoft Windows domains (organized in forests for larger organizations and possibly interconnected by domain trusts). As such, it is a rather "technical" directory.
The Tivoli DS is set up as a directory server for identity management in a heterogeneous environment. Often networks are much more complicated than just a "Windows domain with an Exchange server". Where you have different operating systems, countless applications with own user databases to be integrated and workflow requirements for user management, you are way outside the scope of AD's initial design. While a lot of functionality can be added through 3rd party identity management solutions to Active Directory, you are likely to end up with a hard to manage rag rug of software solutions in many cases and would need to put considerable effort into additional interface programming.
This is where solutions like Tivoli DS along with the bunch of accompanying services like Directory Integrator, Identity Manager or Access Manager close the gap - most of the integration, authentication, authorization and workflow mapping needs are covered by one or the other of Tivoli's products. I would describe it as a rather higher-level "organizational" directory (which of course still has a large number of technical tasks).