Of course modphp would be faster as php becomes part of Apache with this approach. The problem is that not every Apache process is going to serve php. Most of them will be serving static files but will have the overhead of the embedded php library. The real overhead though comes due to that you can't control how many Apache processes serve php and how many static files. Processing php eats a lot of RAM and you can quickly bring you server down to its knees. You could opt for less Apache processes but then you would end up serving much less visitors.

Anyway, Apache these days is mostly set-up with fastcgi or php-fpm due to these issues and this has the added good that you can use the worker or event mpm, though most benchmarks are still with the older prefork mpm.

I use nginx with php-fpm because (a) I find nginx easier to configure than Apache; (b) the configuration required for setting up nginx + php-fpm on Debian and Ubuntu is practically nil; and (c) this allows me to run PHP and Python apps on the same server on different subdomains.

The memory requirements of Apache with mod_php are one of the main reasons people hosting PHP applications use Nginx (or LigHTTPD, although enthusiasm for it has died down). I imagine it is still a common setup to have Nginx in front of Apache serving static content itself and forwarding the requests for dynamically-generated content to Apache.