This is always an interesting conversation. My training and experience is with breeding farm animals but, the principles are the same. Hundreds of traits, important and less so, are influenced by genetics and the environment the animal (or plant) is in. The combination of the two determines what we see.
Now probably none of us are concerned with a pup’s palatability, marbling or dressing % so let’s look at mature size since that is easy to observe. Lots of traits dog bleeders are interested in are hard to measure, I don’t claim any experience there, but the basic science is the same.
Genetics is best thought of as averages, trying to predict an individual outcome is a gamble. If the male and female are of the same breed the genetic gamble is less. If a breed has an average male mature weight of 90lbs and an average female mature weight of 70 lbs you are pretty certain the pups from two animals having those weights will hit pretty close to that.
If you use a male that has a mature weight of 100lbs you will pull the pup’s weight up, but not by 10lbs. At any rate the weights of the parents will pretty much create a high and low range for the pups. You won’t get many outliers. Some maybe, there might be a small male or big female that makes you wonder were they came from, but that’s why they are called outliers.
This is the predictability that comes with purebreds.
Now, do the same with two different breeds and heterosis comes into play, the average offspring out performing what you would expect from the two parents. Not saying the resulting males will all be bigger than the male parent, just bigger than you would expect. Crossbreeding also results in more outliers, a wider distribution, with the average being bigger than what would be expected.
In addition the resulting crossbred animal isn’t able to pass on the improvement that was due to the heterosis, things go back down to the mean.
So for any trait crossbreeding can result in a “better” animal, but not predictably so. You could get a pup from anywhere on that continuum, with the average pup being better for whatever trait. Crossbreeding has a wider range, less predictable outcomes. If you can only select one pup, your chances are better with a purebred.
Now that doesn’t mean a person can’t have a very, very good crossbred animal. It does mean some luck was involved and the traits won’t reliably stay in the next generation. Just enjoy them while you have them, I had a lab/setter cross that I think could hold their own against any dog, and that litter most likely had some dinks.
Line breeding is just the opposite, you breed and select for a trait to lock that in, trying to eliminate any outliers.
Whew, that got too long. I certainly don’t consider myself an expert, corrections are welcome.