The mod_rewrite documentation says that the RewriteBase directive is required unless either of the following conditions are true:
- The original request, and the substitution, are underneath the DocumentRoot (as opposed to reachable by other means, such as Alias).
- The filesystem path to the directory containing the RewriteRule, suffixed by the relative substitution is also valid as a URL path on the server (this is rare).
The first condition is probably met with your Ubuntu setup but not with your Mac setup, since you are using mod_userdir. If you move your files from ~/Sites to the DocumentRoot (default on Mac is /Library/Webserver/Documents), chances are that you won't need the RewriteBase anymore.