Whenever a picture is sent via MMS, a certain amount of compression needs to be done in order for a carrier's network to send it. That compression is meant to ease strain on the network, but in the end it leads to heavy downsizing and increased graininess in pictures.
Hangouts, and most other texting apps, use the "Bitmap.createScaledBitmap" API to produce a compatible picture MMS, but that just gives a crappy, low-quality version of the original image.
Developer Kevin Mark decided to do something about the compression of MMS images and created an Xposed module to change the API used during image compression. The result was XHangouts, and with it comes an all around improved MMS experience for Hangouts.
XHangouts is an Xposed module, so you'll need to have a rooted device with the Xposed Framework already running. XHangouts can be found in the Download section of Xposed Installer. After installation, make sure to activate the mod and reboot your device.
The new API is already set after you reboot, but XHangouts comes with a few more extras. While not always an issue, Hangouts can sometimes improperly orient photos, so XHangouts comes with an option to make sure your pictures are always sent correctly.
There is also an option to change the behavior of your Enter key. By default, it is set to trigger the Emoji keyboard, but you can change it to create a new line or to send your message.
You can see in the test pictures below that the quality of the image definitely increased when XHangouts was activated, so now you should be able to send text-heavy images worry free.