Composted chicken poop is great for a garden. Everything I've seen says do not used composted predator poop on vegetables. Composted poop from predators like cats and dogs can carry pathogens. Plenty of people use composted predator poop on ornamentals, just not on things you are going to eat. But composted chicken, rabbit, cow, horse, pig, sheep, or goat manure is a fantastic addition to a vegetable garden.
Some poop has more nitrogen content than others. Chicken poop is the strongest and rabbit is probably the weakest. Most poop is so strong in nitrogen that it can burn plants if it comes in direct content with the growing plant or roots. Some plants are more susceptible than others to this damage, say squash are more susceptible than corn. This does not mean that it won't burn corn, just that it takes a higher concentration than for squash.
The wood shavings, on the other hand, are high in carbon and very low in nitrogen. The microbes that break down the carbon need nitrogen to break it down. If there is not enough nitrogen available from other sources, the microbes will take carbon out of the ground and use that, not leaving enough free nitrogen available for growing plants. Once the microbes have used the available nitrogen to break down the carbon, it is again available for plants to use, but you can nitrogen starve your crops by putting the carbon heavy material directly in your garden.
The original poster in this thread mentioned green and brown for the compost pile. Nitrogen is considered green and carbon is brown. For material to compost at its optimum, the green and brown needs to be at a certain ratio. If this ratio is out of balance, it will still compost but it can take a lot longer, especially if the ratio is high in carbon. Moisture plays a big part too. If the balance is about right, the compost pile will heat up, getting hot enough to cook weed seeds in the mix. I don't think chicken manure has many weed seeds, but cow or pig, for example, can be loaded with them. So can grass cuttings, straw, or many other things you add to a compost heap.
Straight chicken manure is considered green. Wood shavings are considered brown. Whether the mixure is considered green or brown of course depends on the ratio of chicken manure to wood shavings. It also depends on the conditions in the coop. For example, if you use the deep litter method and enough mositure is present, some of the material will break down in your coop. It should not heat up that much because it should not have that much moisture and usually the nitrogen part of the ratio is very low, but it can partially break down. Different ones of us have different management techniques. The material coming out of a doll house coop that is cleaned weekly is going to be a lot different than the material coming from a coop that is cleaned once a year. Some use droppings boards and some don't. That is why generalizations and blanket statements are risky. You will get quite different results using the wood shavings that are cleaned out on a very regular basis, especially if a droppings board is use, than you would with using the stuff that comes from the droppings board. Anything else is somewhere in between. If you keep the bedding very, very dry you may be able to get a mixture that is actually high enough that it would be considered green but it is highly unlikely. In almost all cases the stuff coming out is high enough in carbon to be considered brown.
Some people successfully put the stuff directly on their gardens. If that works for them, that is great. What techniques do they use? Do they put it on the garden in the fall after the annual cleaning out the coop so it has time to break down over the winter? This is not a bad plan at all. Do they put it up next to the plants or in the middle of the rows? What plants do they use it on? What is the specific carbon nitrogen ratio of the mix they are using? Do they till it in so the carbon material will rob nitrogen from the plants or leave it on top as a mulch so less of the material is looking for nitrogen. When I mulch, I often put newspaper down first to inhibit this nitrogen robbing process. How wet or dry is their climate?
I'm not arguing at all with the people that have developed techniques where they can successfully put the bedding directly on their gardens. More power to them. There are conditions where it can work. I'll compost mine because I don't have a technique that works and I am a big believer in the benefits of compost. I'm just cautioning you to be a bit careful. I'm reminded of a post in a similar thread a while back where someone said they use the litter on their garden then, after some discusson, added another post further down in the thread that said that they compost it first.