I moved a site several weeks ago and added redirects to remove /index.php/ from every page at the same time and traffic hasn't fallen off.
Some things to check
- make sure every single url is the same.
- make sure your non www index page version isn't a parked page (some hosts monetize it).
- make sure your .htaccess commands all work properly, it doesn't matter if it's the same host, it's a different server.
About hosts monetizing the non WWW version of your index page. If you have a redirect in place to send non WWW traffic to the WWW version the host might be blocking that depending on referrer. If you have incoming links to the non WWW version the pagerank may no longer be redirecting = loss of rankings. A sign the host isn't above doing this is to check your error pages for inserted host ads.