One is solution that gets you the best of both worlds is to use a CDN that supports origin pull, like Amazon CloudFront, and configuring the ModPagespeedMapRewriteDomain option in mod_pagespeed (see the section on Mapping Rewrite Domains).
This works as such. When you configure the MapRewriteDomain option, you'll set it up so that mod_pagespeed will change the URL of optimized resources (images, js, etc.) to use the CDN's domain. When the CDN receives a request for a resource it doesn't have, it will fetch it from the origin domain, and cache it (this is the origin pull feature). That way you'll be able to get the benefits of both a CDN for your static resources, and mod_pagespeed's resource optimization features.