Is there any disadvantage of mixing both? Will it add more value? I am planning to first dilute them in water and then apply in my veggie garden. I purchased these as bagged composted chicken and cow manures.
Yeah, mixing them is fine! I looked at the products you got, and they look composted well enough I think the best application method would be directly mixing into the top inches of the soil. I think that's better than diluting it in water, because it will stay in the soil better, and you won't lose as much nitrogen through evaporation/leaching. But in any case, it's composted, so most of the nitrogen is already stabilized until the organic matter breaks down further.
The chicken manure is going to be higher in nitrogen, and if it was raw, I wouldn't recommend it for direct application around some plants, but again, what you have is composted, and so is wide application.
There is no problem mixing both. But if you are fertilizing vegetables, this is NOT a good choice of fertilizer! Do you know how decomposed this manure IS? Even if it were very decomposed it would have too much NITROGEN for vegetables unless you've got just leafy stuff like kale, lettuce, herbs. If your vegetables need fertilizer, now, I'd use a good organic fertilizer with numbers similar to 4-6-5. Less Nitrogen percentage compared to the Phosphorus and Potassium. For the winter, these manures should be dumped on top of your garden soil. Soil organisms will feed on this SHIT, grins, IF it is decomposed...go back into the soil to poop it out, mixing this material into the soil FOR YOU. If it isn't decomposed, the decomposers can use the high nitrogen to decompose this material down to be useable by the other soil organisms. In the spring turn your soil over before planting. I'd also test my soil before planting. Chicken and cow manure are great to incorporate Nitrogen and organic matter into one's soil but it is tough to know HOW much Nitrogen is being added. There is one other thing to take note about and that is are the chickens and cows that donated this stuff on medications of ANY sort? Don't use it if so...only organically fed chickens/cows should be donating shit for vegetables. Otherwise fine for ornamental plants. Chemicals are chemicals. Just because they are obviously 'organic' does not make them safe or correct to use without soil tests and KNOWING as much as you can about the chemical's origins. Lots of weed seeds...weeds have NEVER bothered me but lots of weed seeds will make it through the digestive tracts. Just so you know. That would be another question.