I use the Intent MediaStore.ACTION_VIDEO_CAPTURE video recording method.
Intent
MediaStore.ACTION_VIDEO_CAPTURE
By default, the recorded video is stored as a .3gp file.
.3gp
Yes, you can have an mp4 output format, mp4 is just a container : see this to know what kind of data streams you can store in it.
MPEG_4 MPEG4 media file format
Also refer to this