The start up time has definitely increased after I installed Mountain lion. But, that is because I did not do a clean install. Plus this is the third OS X version that I've installed on my computer, a 2009 13 inch MacBook Pro. When I finally upgrade my current hard drive to a larger hard drive, then it might be faster. That's the only complaint I have so far.
Everything else is faster. I also noticed that Safari uses less RAM than it used to. That I'm very happy with. When I use Safari on Snow Leopard, it took up a lot of RAM and it would slow down very often. Now it's Firefox that hogs up more RAM. I'm also happy with more integrated iCloud into Mountain lion. I wish Lion got that right, but hey better late than never.