When to use 32-bit debugger and when to use 64-bit debugger

Live User mode debugging
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Processes on 64 bit machine (irrespective of 32/64-bit) : use 64 bit Windbg
Others - 32 bit windbg
http://stackoverflow.com/questions/1342099/lost-in-windbg-with-64-bit-dump-on-32-bit-machine

Dump analysis
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1.Use 32-bit tools (debugdiag, procdump,adplus+cdb) to capture dumps of 32-bit processes (whether they are on 32-bit machine (or) in WOW64 mode on 64-bit macine)
Use 32-bit windbg to analyze these dumps

2.Use 64-bit tools to capture 64-bit process dump and use 64-bit windbg to analyze.
http://blogs.msdn.com/b/tess/archive/2010/09/29/capturing-memory-dumps-for-32-bit-processes-on-an-x64-machine.aspx

32 bit process