I am not a professional biologist. Biology was not a strength of mine in high school, so don't take this as absolute gospel. I'll just throw out my opinion in the hopes I get corrected and learn something, or maybe in a positive way add to this conversation.
If we were talking one gene, then this discussion of hybrid would be a bit different. We are not talking about one gene. These complex organisms are made up of many different genes and they interact with each other differently. For example, if a breeder crosses two purebred chickens, the offspring will not all be identical. There will be enough variation in the offspring that the breeder can cull some and select other to continue with the breeding program. If the breeder does not select carefully the quality of his stock will go down. This is not just for show qualities, but also true for egg laying ability, for example. There are just too many different genes in play.
If you cross two different breeds of purebred chickens, you can be real sure of what colors and patterns you are going to get. But you can get small variations in colors and patterns even between siblings. You can get quite a bit of variation in adult size and conformation. You'll have a pretty good idea of what you will get, but there will be variations. There are just too many different genes in play.
If you cross two crosses, there are many different possibilities in color and pattern, partly because different genes react differently when they are present depending what else is present. These color and pattern variations are easy to see, but the same is true for other qualities, egg laying ability for example. If the original hybrids came from good egg laying breeds and the hybrids were chosen for good egg laying ability, the odds are most of the offspring will be good egg layers. Some will not be as good at laying eggs as others. If you hatch out enough, whether purebred, hybrid or just mutts and select for good egg layers, you will probably continue to get good egg layers. But it is a never-ending cycle. If you don't select for egg laying ability, even purebreds will likely not be good egg layers over time, probably a very few generations.
Plants can get a little more complicated. You have many varieties that follow the general rules. If they are purebred, they will pretty much produce a purebred plant that has the same characteristics of the parents. There will be minor variations but they will pretty much breed true. If you cross two specific purebreds, you will get a hybrid that will have pretty reliable characteristics because specific genes are paired a specific way. But when you cross hybrids, there are so many different possibilities of gene matches and they interact in so many different ways, you really don't know what you will get. You might get something that looks like either original parent, something that looks like the hybrid, or you might get something totally different.
Then you have other plants that really complicate the issue. Apples immediately come to mind but there are plenty of others. Apples of a specific variety will not pollinate other apples of that same variety, even a second tree of the same variety. If you have one variety of apple tree, to get any apples, you need a different variety of apple that blooms at the same time so they can cross-pollinate. There are so many different genes in play, you have no idea what that offspring will look like. Sometimes you get lucky, but usually you get a small, twisted gnarled worthless apple. The only way you can get another Granny Smith, for example, is to graft a Granny Smith onto a rootstock. You cannot grow another Granny Smith from seeds. It just doesn't work that way.
