I have a server, its httpd.conf already has some "RedirectMatch permanent" directives in it.
I'm not that familiar with mod_alias, I've only ever used mod_rewrite.
What's the basic difference? I don't see a "L" flag in mod_alias to stop processing rules.
Which one should I use for best practices of redirecting from one sub-domain to another?
Can I use both at the same time and will it be obvious which takes precedence?
mod_alias is basically a simpler version of mod_rewrite. It can't do some things that mod_rewrite can, such as manipulate the query string. If you're able to choose either of them, I don't see any reason that you'd want to use mod_alias.
Is there a specific reason you need to try to use both together?
Apache mod_rewrite & mod_alias tricks you should know seems to be a good article about the two. It notes at one point that mod_rewrite rules get executed before mod_alias ones.