ANI is a Windows-only pointer format that other apps do not open. JPG opens on every device and is accepted by practically every upload form. ANI is at home in animated mouse pointers on Windows; JPG is the usual choice for photos you need to share, upload or print. JPG is lossy, so keep the ANI original if you may need full quality later.
JPG has no transparency, so see-through areas of an ANI are filled with a solid colour, white by default; you can change it under Options. JPG holds a single still image, so an animated ANI does not stay animated. The defaults suit most files. Under Options you can set the quality, aim for a target file size and resize the result.
An animated cursor is converted from its first frame only.