Each type of medium has its pros and cons. Any more, all three are capable of high definition video. There is also a fourth type of medium that is becoming popular and that is hard drive camcorders. MiniDV's are the most common type of medium. They can store one hour of high definition video in 4:3 or 16:9 aspect ratios, or one and one half hours of standard definition in both aspect ratios. In order to capture the tape to a computer, though, it must capture in real time through playback.
MiniDVD's are capable of the same recordable length of time but only certain types of miniDVD's can be re-recorded. Transferring video from a miniDVD to a computer is much faster because you can quickly copy a video file without playback.
Flash memory is the fastest type of medium for camcorders and the memory capacity is much larger than that of a miniDVD. The bad part of flash memory is that it has a limited number of write cycles so after so many times of recording, it will become impossible to read or write to the memory card. This can be a very bad thing if the flash memory is internal. If the camcorder write the information to a removable stick, though, this is usually not a problem. Flash memory's transfer rates are extremely quick but sometimes there can be loss of video quality. Flash memory will usually last a very long time so there is no need to worry about its lifespan.
The most recent form of medium that is still growing is the hard drive camcorder. These cameras have built in hard drives with large amounts of memory capacity that are capable of storing quite a few hours of high definition video in both full screen and wide screen aspect ratios. Transferring video clips from the camera to a computer is as simple as dragging and dropping a file.