Haha, as much as I am totally charmed out by the resemblance (feels like my pixel art style had kids or something : D ), I agree with this point! At the same time this kind of snappy run is right in line with my preferences (hmm, I guess why), so I like that particular direction.
Right now I feel that it's a bit TOO snappy, whereas the run I did was me trying to create maximum smoothness and readability without using an excessive amount of frames, I feel this mainly borrows the snappiness from mine, but not the small details I did to smooth it out.
So chuu CHEW <3 I'd suggest you actually try to reduce the snappiness - every frame where something appears to stand still compared to the last one - change something just a little, so that it acts like an inbetween instead of a pause. I'm mainly talking about arms and legs here. I'd like to see this smoothed out generally, actually. It would be fitting for an explorer-kind of guy as well, seeing as that kind of guy would probably be a little heavy, thus having to more bounce-jog than snappy-run. (grammar successfully destroyed)
Soo.. More joggy, less snappy, more smooth! Also more bounce! Give this guy some own character, think about who he is and go from there! See if you can get some movements in there that convey some of his character!
Also you know I'm totally impressed by all of this, I had no idea you'd GET the animation/pixel art thing so fast. There is still much to be learned, though, so lurk the forums and POST more! Post that mailman guy!