Encoding (and decoding) h.264 is a highly intensive process and requires a large amount of processing power. The simple fact is not that your camera has more processing power than your laptop (it doesn't) but that it has a piece of hardware that is dedicated to the job of encoding and decoding this type of video.
Your laptop has a general purpose processor (the CPU) that has many times the processing power of your camera but it effectively has to emulate the abilities of the hardware decoder that your camera uses. As I mentioned this is a highly intensive process and if the software being used to decode the video is poorly written then it will behave in the fashion you are seeing.
Most modern computer systems have a dedicated graphics card, part of which is also dedicated to hardware video decoding of this type of video. More lately this has also appeared on processors, specifically Intels latest generation i-series processors. Using these decoders takes the workload away from your processor and you get nice smooth video playback.
Firstly I would look for trying to use a different player for your files as VLC support for hardware video decoding is somewhat limited and may not be working for the files you are giving it.
As it is a .mov file I would try downloading either the QuickTime player from Apple or the Divx Player as I believe these may be able to make proper use of the hardware video decoder.