When comparing BPMS one usually needs to consider the particular project requirements and situation. I cannot cover all aspects here, but let me add some thoughts.
A very significant difference between Activiti and Stardust is certainly the size and maturity of the code base. The Stardust code base is more than 5 times the code base of Activiti. Under the hopefully fair assumption that the Stardust team is not coding 5 times less efficiently, Stardust is more feature rich.
Some statistics from Ohloh (@see https://www.ohloh.net/p/eclipse-stardust and https://www.ohloh.net/p/activiti):
Activiti has had 4,388 commits made by 79 contributors representing 438,155 lines of code
Stardust has had 8,312 commits made by 38 contributors representing 2,538,729 lines of code
Activiti took an estimated 116 years of effort (COCOMO model) starting with its first commit in June, 2010 ending with its most
recent commit 3 days ago
Stardust took an estimated 726 years of effort (COCOMO model) starting with its first commit in December, 2011 ending with its most
recent commit 7 days ago
Activiti has a codebase with a long source history maintained by a
very large development team with increasing Y-O-Y commits
Stardust has a young, but established codebase maintained by a
very large development team with stable Y-O-Y commits
Both products originate from the Java world. Activiti seems to keep focusing primarily on the Java community and is sometimes positioned as BPMS for primarily for Java developers. Stardust has invested strongly into interoperability with the .NET world and is also targeting an audience that is not too familiar with Java, for instance with the web modeler. (SunGard has a number of .NET products that it integrates with the commercial Stardust version).
Activiti has a young code base and was designed for BPMN2. Stardust has a 13+ years old code base and is gradually supporting more and more BPMN2 elements.
Greg Harley's comment is not entirely correct.
there is still a commercial product of Stardust, the Infinity Process Platform (IPP). the code bases are synchronized and merged regularly. Both version have no license fees. Support from SunGard is available for the commercial code base. In terms of functionality and maturity Stardust and IPP are almost equivalent.
As a startup CARNOT had its primary market in Germany, Austria and Switzerland and additional traction in the Americas. After the acquisition SunGard rebranded CARNOT to Infinity Process Platform. So it has always been available as a standalone product, recently also hosted and as a Paas/Saas offering. In the Gartner Magic Quadrant 2007 SunGard was ranked 2nd in vision with a strong ability to execute. Later SunGard was not included in the Gartner quadrant anymore because SunGard is primarily offering products to the Finanacial Servcies and Energy industry. IPP is embedded in more than 60 SunGard products and has hundreds of installations worldwide.
Activity has a diverse group of committers and an active community. Some strong contributors like the founder and project lead Tom Baeyens or those from Camunda recently left the Community and started/forked new projects.
Stardust was first release in Summer 2013 in the Eclipse Kepler release. Hence so far its community is young and not very divers at this time. There has been significant growth during the last few months though.
Activiti is under the Apache license. Stardust is under the Eclipse Public License (EPL).
