libmp4v2 | Automatically exported from code.google.com/p/mp4v2 | Audio Utils library

You can use MP4Box from GPAC to analyze the MP4 box layouts of both files. As seen here, the bad file is missing the SPS/PPS data in the avcC box. The same NAL units are most likely stored in the NAL units as well, but the specification requires them to be also present in the avcC box (some players handle SPS/PPS inlined in the stream but that is a bad practice since it breaks seeking and what not since you don't know which sample groups reference which parameter sets upfront).

A quick google search for libmp4v2 gave me this example which shows how to actually call MP4AddH264SequenceParameterSet/MP4AddH264PictureParameterSet to provide the SPS/PPS, while you only call MP4WriteSample which could be the issue.

My subjective opinion - I have never used libmp4v2 but if you don't know how to use it too just use ffmpeg instead - more examples and the community will be bigger. Muxing H.264 into mp4 is quite simple, again lots of examples on the internet.

SUMMARY

1. MP4 requires the SPS/PPS information to be in the avcC box - some players may be able to decode the stream if these units are put inline with the samples, but to conform to the specification, one should always have the avcC box present, otherwise a player is free to fail to play the stream.
2. Depending on the library used, there may be different techniques how to signal the SPS/PPS to the muxer, but as seen here with libmp4v2, one must use P4AddH264SequenceParameterSet/MP4AddH264PictureParameterSet. To obtain the SPS/PPS data one should parse the bitstream. This varies depending on the bitstream format (if annex b format with start codes or avcc format with interleaved lengths are used - see this for more info). When the SPS/PPS info is extracted it should be passed to the muxing library.
3. Handle SPS/PPS change with care. The specification actually states that you can have multiple stsd stream description boxes and then reference them, but as far as I recall, Windows Media Player handles this poorly, so if possible stick to a single SPS/PPS set. One should be able to configure the encoder not to emit duplicate SPS/PPS entries on each keyframe.