Camcorders and digital cameras are designed to be best at there individual jobs. Pretty much all video camcorders have a Photo button allowing the capturing of still shots but there are usually limited to the video resolution the camcorder is set at at the time.
Digital cameras of the compact kind might have a video function but again limited in screen size, frame rate and record length in addition to no control over zoom and very poor audio.
Some Digital-SLR cameras are now shooting in HD with a little improved sound. This would also give you interchangeable lens, sharper optics and outstanding still photos.
The question to ask yourself is...Is video the primary or is great photos more important. Then decide from there the features you need with the other as secondary.
Battery life on the Camcorder and the Digital-SLR should be pretty high with the compact cameras being very short along with short record lengths.