I have an S3 (for now; still deciding on whether I wanna return it or not) so I'll just list what I've been experiencing:
The main issue with using MX player is making sure that you've got HW or preferably HW+ going on for your decoding. If you use software decoding, it's fucking garbage.
That's also the problem. Every group I've come across besides Horriblesubs can only do software decoding on the phone, unconverted. Horriblesubs is the only .mkv container group that I've come across that actually works on it completely unconverted. For Horriblesubs, I've been playing Jinrui on my phone. I happened to have the first four episodes in 1080p, and then I downloaded the others in 720p. The 1080p episodes played pretty good visually, but the audio would get ahead of the video after some 5-10 minutes of viewing. Nothing a light tap on the progress bar wouldn't fix, so not really a big deal. As for 720p stuff, I have literally encountered no issues playing it back, but it wasn't particularly high bitrate.
To get other groups besides horriblesubs working (ie gg's Chuunibyou encode), I had to run em through XMedia Recode. All I did was strip out the chapters (not sure if it does anything really) and convert them right back into MKV at the exact same resolution and probably with roughly the same codec. The resolution was 720p (iirc), and I had no issues playing it back.
As long as it's not Appleseed or some shit, I think it can work unconverted anime just fine... as long as it can actually read the format without automatically doing SW decoding. I doubt it can play really high bitrate encodes, but I don't really see a point in those on a phone anyway. Just being 720p looks damn good enough on that screen already, and the playback looks pretty damn good for Jinrui; very good colors and good quality.