I know that they come from different sources, but is there a reason to prefer one over the other? Are they appropriate for different tasks?
The values of manure and organic fertilizers in general, are often based on the relative amount of nitrogen (N), phosphoric acid (P) and potash (K) they contain.
Some common types of manure compare as follows (in N/P/K terms):
Dairy Cow: .25/.15/.25
(Sources: Rodale's All-New Encyclopedia of Organic Gardening, An Illustrated Guide to Organic Gardening, by Sunset Publishing, and the Rodale Guide to Composting. via http://www.plantea.com/manure.htm)
Horse and cow manure are also humus-rich while sheep manure is easier to handle (http://www.vegetablegardener.com/item/2427/using-manure-to-fertilize-your-garden). Dairy cow manure is often favored over other types of fertilizer, as it is low in nutrients and can be applied in endless quantities with no detrimental side effects (http://www.lawncare.net/stay-green-with-manure-fertilizer/).
You also have to take acidity into account. Acidic manures are great for fertilizing tomatoes, but not what you want for carrots or something else, for example.
Although high in nutrients, because sheep manure is deposited in the fields, it is not mixed with straw or hay like horse or cow manure, and is therefore not as good a soil conditioner. It is also rather dry and takes longer to break down and release its nutrients. However, it has a much lower odour than either cattle or chicken manure and, as pointed out, is easier to handle.
My own soil is very light and free-draining - too light, in fact, because it dries out very quickly, requiring a lot of watering and fertilizing, and it loses nutrients much faster than a heavier soil. Having tried horse, chicken and cattle manure, I have found that the best manure for this type of soil is cattle manure, as it bulks it up and gives it more substance. Horse and chicken manure - and, probably, sheep manure - are more suitable for lightening heavy, clayey soils.
Any manure is good to condition soil. But, sheep is very high in nutrients. After applying any manure of cover crop, it's advised to wait two weeks for it to begin to break down. Sheep will cause a wild growth at first, like a kid who's a candy freak, then slow down. Organic fertilizers are good for 3 years, whereas chemicals fade quickly. Do not forget in Fall, to plant a cover crop unrelated to anything you're putting in now. We can plant chickpeas, turnips and so on as cover crops. Daikon radishes will root as deep as 8 feet, turnips as deep as 6, and put humus into the lower levels while recovering fertility too deep for average crops. When they rot, they leave holes filled with very fertile soil. I would recommend a light application of sheep (one ton/acre) but up to 11 tons of cattle per acre for plants with a high-nitro need like greens and maize. this is ultra very old-fashioned farming; what was old is new, agronomists say. Manure is a fast track to carbon in the soil, but cover crops put it deep and keep it there. Niio