What is the difference in the number of developers actively
particiapting in a) PHP and b) Microsoft ASP.NET communities to
improve these technologies.

The question is born of an interest to know which community has the
greatest resource at their disposal to innovate and accelerate the
respective technologies and therefore which technology over the medium
term will supercede the other through better design, features and
stability.

Are you assumimg more resources are likely to lead to more innovation ?
Or that systems supercede other systems through better design ?

"Are you assumimg more resources are likely to lead to more innovation ?"

Yes and no - I am perceiving that more resource can create a greater
melting pot of ideas, feedback and analysis - I believe this fuels
catalysts of innovation.

"Or that systems supercede other systems through better design ?"

The use of 'or' makes this inquiry difficult to answer as I don't see
the questions linked that way and I'd prefer to treat them
independently of one another...

Systems don't just supercede others through design.  The reality of
business and economics plays its part (think VHS and Betamax). 
Factors such as installed user base, marketing, commercial
relationships, encumbent investments, barriers to entry (price,
technology embargoes), politics (think lobbying) and the ability to
change or integrate choice of technologies will affect any
technology's chance of superceding another competitor.

If there are more people using and improving PHP will this mean that
ASP.NET will fail to keep up if the community of PHP is greater than
ASP.NET... but my google question is to know the difference in the
size of these two communities - then it's anyone's guess ;-)

ASP.NET has commercial support and is more money-driven. ASP.NET
development often associated with commercial tools and modelling
approach. ASP.NET requires less secure, stable and more expensive
windows platform than classic LAMP / FreeBSD approach (I use windows).
For rapid application development ASP.NET is slow, very formalized,
strong typed (i.e. not intuitive) and it's database API is too
overburdened to my liking, but ASP.NET has some interesting concepts
and native IDE support. For long-term, automatic code
management/testing/modelling/reversing this approach is probably good,
but I didn't see any tools for that yet.

PHP on the other side is positioned as low-end solution, easy to use,
not expensive (sometimes even free), but hard to maintain in complex
projects, because of poor support of complex programming paradigms and
mostly open-source than money-driven. PHP is very easy to start and
therefore there are many PHP programmers, but not many of them are
professionals. PHP is not studied in combination with UML or other
critical approaches for long-term complex projects and this leads to
low overall quality of many open-source PHP programs. Developers are
moving from PHP to Java or .NET because they prefer more well-paid
jobs. As a PHP developer I'm switching to ASP.NET for the same reason
and I have much to say about how I'd like to see the process of PHP
development. For example better PHP integration with Java, .NET and as
a general scripting language - not web-only, more resources to be put
in developing free !basic instruments for PHP (in debuggers,
profilers, test-suites/environments for continuous intergration -
?eclipse). And as of language itself PHP needs refactoring for new
web-generation with transparent XML/XHTML2/XSLT support, functionality
and documentation cleanup and revisioning. Environment tuning
on-the-fly via functionality layers which can provide extensions for
language constructs and concepts such as sessions, object persistion
along with standard function pack via .dll and php.ini (php.xml and
phpapp.xml)

To be short - PHP is simple, but lacks commercial support and hard to
maintain in a long-term perspective without special skills which many
PHP-only developers lack. Developers are attracted by simplicity and
low costs (or no costs at all), fast development process.

ASP.NET is commercial, it has a concept of application - not just
script, has a lot of documentation and tools. If you have money and do
not want to tightly participate in language development - that is
probably the best choice.

IMHO. =)