I have asked myself that same question. Today I have been trying to find a post where I'm pretty sure I read the answer a long time ago. So far, I can give you some links to the things I have read until now:Difference between mint-flashplugin-x64 and flashplugin?
This one is a bit of a discussion. There are several questions asked in here, but as for this date, there are a few replies, but is still "open".Difference mint-flashplugin & flashplugin-nonfree
This one is "solved". It has just one reply.LMDE - Videos - Flashplugin
This is actually a question about a problem regarding Flash, but it has some information about both plugins. Basically says that it's okay to install the plugin from Adobe instead of Mint's.
Here is also a quote from Mint's blog:
Which Flash package is the recommended one?
–> We recommend mint-flashplugin (32-bit) and mint-flashplugin-x64 (64-bit) which provide the latest version of Flash Square from Adobe. Upstream packages from Ubuntu are not recommended (they tend to be obsolete and run in 32-bit mode on 64-bit systems) and the same goes for nspluginwrapper. Do not install these packages in Linux Mint unless you’re experiencing issues with Flash or crashes in Firefox.
Source: Mint 10 & LMDE FAQ
In a few words, all I have read until now says that both plugins seem to be fine, but the proprietary version seems to solve some problems some people have had. It is also given support for that one, since any modified version won't be supported by Adobe (obviously). Also, flash-installer is not recommended.
I will keep looking for that post. I hope I can find it. If I do, I'll post it here. In the meantime, I hope what I have found is somehow useful.
I have found this response to a similar thread
. Here seems to be the answer...
Also, I found this: Flash 11 on Mint 11 Katya and other Ubuntu 11.04-based distros
. It's a tutorial, but it mentions something:
Adobe does not provide .deb files for Flash anymore.
This being said, I would guess it has to do with that (above there's also a post that mentios something like that). In a time where Adobe no longer provides the package needed for Mint, it was needed a package to be downloaded. I actually remember I couldn't download flash from Adobe's web site. So, it is probably because of that. Plus, wrapping 64 bit version with the 32 bit, that sounds like trouble.
So, I guess this is it. I might look deeper into this, but maybe later. Still, I hope for now all this answers your doubt.