If you have read any of my posts you have probably noticed that I am very partial to windbg and the debugging tools for windows. I often get friendly nudges from the developers of debugdiag when I suggest using adplus and windbg on internal discussion lists, and to be fair I have to beat on the drum a bit for debug diag as well.
My answer to the question "Should I use DebugDiag 1.1 or Windbg" is both... it just depends on the scenario. I often lean towards windbg but to a large extent that is because that is what I use all the time, so in many cases where both fit the bill equally well I simlply haven't invested the time to see how it can be done with debug diag and therefore I suggest what I know works.
Before I start the comparison, I just want to mention that dumps created with debug diag can be analysed in windbg and vice versa. They use the same APIs and create the same types of memory dumps. Where they differ largely is how you configure them to gather these dumps and logs, how you analyse them in the different tools and by the fact that DebugDiag has a nice feature that allows you to monitor memory leaks in the process.
I personally use debug diag to gather dumps for native memory leaks, and I use it to analyse asp and other native issues in conjunction with windbg. For everything else I use windbg because a) I like the logs that adplus creates and b) I like the fact that I have full control and can execute any commands I want.
Having said this I know that it is much easier to gather dumps in debug diag, and it has excellent automated analysis features which is great if you don't do post-mortem debugging on a daily bases, so I would strongly recommend trying both and making up your own mind about which one fits your style best.
Where do you get the tools?
Debug diag can be downloaded and installed here.
Windbg comes with the debugging tools for windows which you can download here.