What
Zachman is like the map at a low resolution.
TOGAF is like the directions on the map that will lead us to some destination (it may be a good or bad destination).
FEAF contains specific information such as the reference models which act like the road rules and speed limits and communication protocols of our mobile phones, etc. (these are the sensible and logical constraints).
MODAF / DODAF and other defense architecture frameworks describe how our vehicle, which we are using to undertake our journey, is constructed, supported, used, etc (say a bike or a car).
When
Always refer back to Zachman when you are lost. (Overcome with complexity).
Refer to TOGAF at specific milestones in the journey. (Preparing for reviews, checking completeness of the architecture, etc.).
FEAF reference models for what technologies, constraints, resources, etc that can be used in the architecture.
DODAF when redesigning or designing or specifying explicitly a ‘widget’ in the architecture. (Widget may be a solution agnostic architectural building block or a solution dependent solution building block).
References:
A Comparison of the Top Four Enterprise-Architecture Methodologies -
http://msdn.microsoft.com/en-us/library/bb466232.aspx
TOGAF
http://www.opengroup.org/architecture/togaf8-doc/arch/p1/enterprise.htm
http://www.integrationconsortium.org/?page=TOGAF9
Gartner Architecture Patterns:
http://www.gartner.com/DisplayDocument?doc_cd=125007
http://www.opengroup.org/architecture/togaf7-doc/arch/p4/others/others.htm
http://www.software.org/pub/architecture/fwhome.asp
Blogs:
Serge Thorn's IT Blog - http://sergethorn.blogspot.com/
http://blogs.ittoolbox.com/eai/qos