It depends really on what you want.
A photo is two-dimensional, a painting is (or rather should be, as my husband's are) three-dimensional. In a painting the dog's features should "come out" of the painting, right at you. Its eyes should follow you round the room.
A photo on canvas has a limited lifetime, as the colours will fade, even if not placed in direct sunlight. It can also be affected by being placed near heat, or a damp atmosphere. It will be a lot cheaper than a painting, but has a much much shorter life.
A painting, if done with acrylics anyway, won't fade and will last a very very long time. It will even withstand central heating, damp etc without any detriment whatsoever. Water colours will fade, pastels will fade, and oils - well, oils would last, but not many people paint in oils nowadays as it takes so long to dry, and because of the health hazard.
If you do go with a painting, any reputable artist won't be looking for one good photo, but will want several photos, taken from different angles, in order to build up the full three dimensional image of the dog. Any artist who doesn't do this will likely only paint a two-dimensional, limited view of the dog. And they don't have to be "good photos" just photos which show its profiles, eyes, nose shape, coat texture etc.
