<p>After having looked at each of these two projects, it seems that both are VERY similar. Both run on top of the CLI, both have python style syntax, both use .NET instead of the standard python libraries.</p>

<p>So, what are the differences between them and advantages of each?</p>

The main difference as I see it is that Boo is statically typed, meaning the type of a variable is inferred on its first assignment and is fixed from there - while IronPython has the "real" dynamic behaviour of normal Python code.
IronPython
is officially maintained by Microsoft now and
targets the new Dynamic Language Runtime in version 2.0. I suspect because of it's statically typed nature Boo might be faster. I don't have much "real" experience with that though ...
IronPython also reimplements lots of the python standard library so you can run lots of python software without change on IronPython (e.g.
Django
).