I am working on a Rails 3 project which was using Mongrel as web server but now I changed it to Passenger web server. And because of this my application respond very slowly.
So I want to know about the performance difference between these two server in production environment.
First of all, Passenger shouldn't be too slow. Unless you're dealing with some significant traffic, I imagine any inherent performance differences between passenger and mongrel shouldn't matter too much. Most likely, the slowness is caused by the way you've got passenger configured.
Does it respond slowly only when you haven't sent a request in a while? If so this should help: Slow initial server startup when using Phusion Passenger and Rails
I remember having this issue with passenger a while ago, and resolving it. I don't remember exactly what I did but if you google it I do know there's a lot of info, so I'd start with that and update your question once you have some more specifics.