Powdered food colors, liquid food colors, and paste food colors all use the same dye chemicals. The only real difference lies in how much dye is included in a particular amount of each dye. You will have to use larger quantities of a more dilute dye to get a similar effect. Because most food colorings are acid dyes, they work pretty well as a textile dye on wool, though the results are not as satisfactory or colorfast as what you will get if you use excellent wool dyes, such as Lanaset dyes or Washfast Acid dyes.

Different brands of food colorings contain different proportions of dyes from a very limited list. For example, one red food coloring might be nothing but red dye, while another one contains a red dye plus a yellow dye, while another might contain two different red dyes. Since some of the food colorings perform more satisfactorily than others, some color mixtures will be better than others. However, since there are so few choices for each color, there will not be a great deal of variation from one brand to another.

Overall, aside from those factors, one form of food coloring dye will be similarly successful to either of the other forms, in dyeing a textile fiber such as wool. In any case you will probably be using a much larger quantity of water than food coloring. 

The ninety different colors sold under the brand name "Crystal Colors" are mixed from no more than seven different synthetic food dyes, plus, perhaps, an even smaller number of natural food colors. If you could obtain each of the FD&C food colorings in pure form, you could mix every one of those colors yourself, given enough trial and error. They appear to be much more concentrated than the colorings that you can buy in the grocery store, so they are probably significantly cheaper per gram of dye, even though they cost more per container. The pearl luster colors are made of either food-grade mica or fish scales, either of which can be mixed with an acrylic fabric paint binder and used as a fabric paint, but neither of which will work as a true dye.

Also see:
"Using Food Coloring as a Textile Dye for Protein Fibers".

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