It would depend entirely on the colors used. One color hybrid can vary drastically from another even if it seems like they would produce similar offspring! Heck, cross the right colors, you can get dozens of outcomes just from the same male and female alone.
If you are interested in learning color genetics, I recommend playing around with the
Chicken Calculator and reading
this page created by the same man who made the Calculator. If you find yourself enjoying the subject, I can also highly recommend the book Genetics of the Fowl by F.B. Hutt. While it can seem complicated at first, once you've been at it a while, it becomes simpler. There's quite a bit that goes into making a chicken one color or another - you start out with a base color gene, one of the 7 located at the E locus, which basically determines where black goes and where color goes - take for example the Wheaten gene. A bird who has a Wheaten base will have black restricted only to certain parts of the body - in hens, it is restricted to just parts of the wing and tail and ticking in the hackle, while in the male is is restricted to the breast, legs/fluff, and tail. Then there is the S locus - which contains the alleles for Silver (S - white color) and Gold (s+, gold, red, and brown shades). All birds will be either Silver or Gold, which basically builds on the E locus base color and fills in the parts that ARENT black. So to build on the Wheaten example I mentioned beforehand, let's say these hypothetical Wheaten birds are Gold at the S locus. The female will be generally whiteish with a gold/brown wash over the hackle, tail, and potentially the back/wings depending on breeding. The cock will be gold on the hackle, wing bar, and saddle. And then of course beyond this there are genes which cause white to appear over the bird's existing patterns (Barring, Mottling, and Dominant and Recessive White genes are all examples of this) and genes which modify where black occurs, such as Dark Brown, Melanization, Columbian, Pattern Gene, and so on, which in various combinations cause patterns like Spangling, Lacing, and Penciling. Then there's dilution genes, like Blue, which is a diluter of black pigment. There are... well, there are a LOT of genes.
Of course, you don't necessarily NEED to know genetics to breed. It helps, and it will explain situations that might crop up like "How did Blue X Blue produce not just Blue but also Black and Splash offspring?" or "Why did my cross of Red cock over Barred hen produce only Barred sons and only Black (with red leakage) daughters?" but, in many cases, you can simply breed by hatching a LOT of offspring and choosing whichever ones you think further your goals most. Let's use Red as an example - in this example you have a population of red birds, and you hatch, say, 30 chicks from them. 5 of them have a lot more and richer red than the other 25. In this hypothetical example your goal is to make birds with a deeper, richer red, and so in order to produce more red chicks, you choose these redder birds to breed with. And you will most likely have a relatively easy time of selecting over the generations for redder birds simply by removing all offspring which don't show proper coloration, without knowing a lick of the genetics behind the colors.
