I don't think anyone can answer this definitively for you. It depends on your web server configuration, operating system and filesystem choices, complexity of your SSI usage, other competing processes on your server, etc.
You should put together some sample files and run tests on the server you intend to deploy on. Use some http testing tools such as ab or siege or httperf or jmeter to generate some load and compare the two approaches. That's the best way to get an answer that's correct for your environment.
Using PHP with mod_php and an opcode cache like APC might be very quick because it would cache high-demand files automatically. If you turn off apc.stat
it won't have to hit the disk at all to serve the PHP script (with the caveat that this makes it harder to update the PHP script on a running system).
You should also make sure you follow other high-scalability best practices. Use a CDN for static resources, optimize your scripts and stylesheets, etc. Get books by Steve Souders and Theo & George Schlossnagle and read them cover to cover.