... sure, you COULD proxy, but it will trombone all the traffic through your server. It will also mean the destination server will need some magic configuration in order to trust X-Forwarded-For and/or X-Real-IP from your server.
Redirects are usually the better choice.
(Note: I'm assuming by "another server" you mean a completely other server, like if I wanted
http://hoopycat.com/reddit/ to actually be
http://www.reddit.com/r/hoopycat/ or something. If you mean "another server" like "I've got a couple applications on this server and a couple on another server and I want to make it all work like it's one big happy server", then yes, proxy is the right tool.)
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