I know this is very late to the original post, but I have been looking at the same problem and have experience of various external recorders, so thought it would be of help to anyone else with the same question! My camera is a Canon EOS 550D, so not exactly the same, but close!
1) the internal mic is terrible - as is the firmware. The first thing to do if you are shooting video is to set your camera up for MagicLantern (this may not apply to the 6D, but certainly to the 550D). This gives much more control over the audio recording, eg I can now record ext mic; left internal, right external; etc, set recording levels turn off automatic gain control etc etc.
2) personally I like the dedicated sound recorder option - I have three available to me (I don't own any of them, but various voluntary work I do gives me access as and when needed). My options are a Zoom H2N, a Zoom H4N and a Marantz PMD661. My #1 choice is the Marantz PMD661 - it's also the most expensive! Why the marantz? It is the only one of the three that has line out. Both Zooms only have headphone out. This means a) a splitter cable if you want to monitor from the recorder, and b) adjusting the headphone volume changes the recording level for the camera! The Marantz suffers neither of these and has a really nice sound quality.
The H4N and the Marantz both have 2 channel XLR inputs, so can be used with external balanced mic sources, which the H2N can't. All of the recorders really need an ATT cable to attach them to the camera mic in, though with MagicLantern this can be avoided to some extent by reducing the mic gain from its standard -23dB to 0dB.
A final point to consider - if using an external recorder, and you have at least reasonable video editing software then you can use a clapper board (or similar) to create a synch signal on your camera audio and recorded audio, then synch them in your edit, rather than feeding the output of your recorder into your camera. More work, but almost certainly better quality audio and you can place the recorder exactly where you want it instead of being limited to your lead length.