Is the master branch on https://github.com/monero-project/bitmonero considered to be stable enough at all times to use it for nontrivial amounts of Monero, or would you rather recommend to stick with the official binaries from https://getmonero.org for that, and use the master branch only for smaller amounts?
Is there a compelling reason to switch from the 0.9.4 binaries to the current master?
Unless you understand what has changed in the master, I'd advise to use the stable release binaries, as those have been tested prior to being tagged as a release.
If you just want to compile from source you could use the same source as used for release (0.9.4 source).
If security is your concern, the binaries can be be verified by their hashes which are published and pgp-signed by the devs.
To answer part of your question, the Monero devs recommend that you stick to tagged releases. So compiling from the head master branch is never recommended unless you are testing or really know what you are doing.
However, you've missed a third option that really is the best of both worlds when it comes to being both paranoid and wanting stability. Namely: compile from source from the latest tagged release.
Doing so is as simple as compiling from the head master, with one extra step. After you get the source and change to that directory
$ git clone https://github.com/monero-project/bitmonero
$ cd bitmonero
you can choose to switch to a tagged release
$ git checkout tags/<tag_name>
For example, if you wanted to switch to v0.9.4, you would do
$ git checkout tags/v0.9.4
If you aren't sure the latest tagged release, you can view all releases with
$ git tag -l
For more information about checking out tagged releases, check here: https://stackoverflow.com/questions/791959/download-a-specific-tag-with-git
I'm not a Monero developer, but as a general recommendation I would only use the official release binaries from the Monero website when dealing with non-trivial amounts of XMR.
When dealing with live code, you have no idea if the last commit introduced some fatal bug. The code that's released to the public has undergone testing and is what I would use when dealing with large amounts of XMR.
