A couple of answers:
ASP.NET MVC should be faster.
Why:
Regular PHP is interpreted and as such is the slowest around.
.NET is a JIT environment like Java the performance of .NET is within 5% of C / C++ or it is said to be.
Microsoft is investing heavily to get the performance of .NET as good as possible.
Some benchmarks:
https://www.codeproject.com/Articles/212856/Head-to-head-benchmark-Csharp-vs-NET
But:
Benchmarking anything meaningfull is hard.
So way to long answer:
Please keep in mind the PHP framework speed is interesting but if you look at something that actually hits the database then your performance will tank hard. So things like caching and serving static pages is usually the way to go for really high performance.
This can very easily be done in all sorts of ways.
This is a link that i found on the performance of PHP on Apache vs IIS with a drupal install with a site codebase:
https://groups.drupal.org/node/234373
There is also a project called Phalanger which is a way to get PHP code to run on the .NET Framework.
It's not 100% feature complete with the latest PHP versions:
https://www.php-compiler.net/blog/2014/phalanger-4-0#more-969
An example of benchmarks with wordpress on Phalanger
https://www.codeproject.com/Articles/396035/Improved-WordPress-performance-with-Phalanger
This is comparable with Facebooks Hip Hop VM, which is also running a sort of PHP compiler in a VM
What does all this tell you about the performance, not really a whole lot because there is also things like databases and database drivers to be taken into account and loads of other goodies :)
And ofcourse the way this framework does it's thing it's not really php but a php extension.
Which should make up for a bunch of inefficiencies.