Basically, you have three options:
Livestream
The camera doesn't record a thing. It instead immediately uploads it (through a secure channel) to your military base, and the recording is mad serverside.
Advantages:
If anyone manages to steal the camera, he will just steal a nice satellite/3g connected camera with a send-only apparatus. While this might be useful to reverse-engineer the technology used, your enemy will have no footage of your operations whatsoever.
The live feed can also be used by commanders to make last-minute decisions and have a tactical advantage.
Disadvantages:
If the enemy produces a jamming signal strong enough, you will have no records of the camera. This can be also used as a decisive hit to your intel capabilities, if your generals are using the live feed to take decisions in real time.
The signal could also be used by a technology advanced enemy to triangulate your soldiers' position. (thanks Agent_L)
Recording
The camera records everything, and all is encrypted on disk, using a system like Bitlocker or similar. The recording can then be reviewed safely at the base.
Advantages:
All footage can be recorded in high quality, regardless of available bandwidth or connection loss.
Disadvantages:
The enemy may be able to capture your soldiers and force them not to disable the camera, so they would (theoretically) be able to retrieve the non-encrypted datas still stored in memory. With modern cryptography techniques, this could amount to a few minutes, seconds, or even a few frames of recording, so the advantage of this for the enemy may vary (thanks MichaelK, André Paramés).
Internal storage size will also limit the quality/recording time of the camera. This becomes important for older (less space) camera models or very high resolution cameras (thanks Taegost).
Mixed
This is the system I would use. It involves a bit of both, and consists into recording everything, uploading all the recorded data to the base, then deleting all data already sent.
Advantages:
No quality loss, recording will take place regardless of signal, basically the advantages of both approaches combined
Disadvantages:
If the enemy jams the signal for long enough, you will fall back to the "Recording" case, as data never gets uploaded to the server.