Things to consider before you select chat or shoubox for your website

If your website is on shared server, this server will most probably have problems handling chat traffic because of limited hardware resources (on top of it see 3.).
If your website is on dedicated server but has limited memory and/or has only standard apache/mysql installation, it might have problems handling traffic (on top of it see 3.).
If server is not properly configured, high traffic can bring server to halt/crash (usual case for basic apache/mysql configuration when running out of resources).
If your chat application code and queries are not optimized, chat can require 5-10 times more server resources then necessary.
If your server internet connection is slow (or has too many hubs on the way) then all responses are slow and that is not suitable for chat application.
Problems can be visible sometimes with as little as 10 chatters, depends on server hardware/software configuration, current server load, chat/shoutbox refresh rate.
Chat will use your bandwidth, so consider your limitations there.
Your shoutbox is running fine so far? Refresh every 4 seconds? Is it much better then chat? When your visitors volume increases, see 3.