Both are build for more meat production, so not likely.
Actually, there are some breeding programs resulting in rabbits better than either of their purebred parents, assumed to be due to hybrid vigor. (This type of breeding produces cornish cross meat chickens, most of which are gross thanks to Big Ag, but not all crossbreeding results in monsters!) In rabbits, a Californian x New Zealand cross is frequently used in this way, though its success very much depends on which genetic lines of cals and NZs are used.
There are also breeding programs called terminal cross breeding, in which the animals produced by crossbreeding are bred with a third breed; the offspring are the terminal crosses, which outperform all the original breeds but will not breed true themselves.
Also focus not on meat production, but on healthy animals that are good mothers and able to raise the whole litter they give. Production as a breed goal costs you in health, feed and other extra needed care. The same problems are evident in other species production breeds. It is not a road you want to follow for both your own health, costs and more work as well as their health and wellbeing.
You
can select for both meat production and health; it is not necessary to choose one at the loss of the other, at least over time. It's true that focusing on the most important characteristic to you, one at a time, is the fastest way to fix that characteristic. However, if I had a healthy doe that consistently produced litters of only 2-3, that would not be the only doe I kept if I was breeding for meat! The trick is to juggle the best of several characteristics. When you have more than a couple breeding does, you can compromise lightly on some things and use the strengths of particular does as counters to the weaknesses of others. It does take time and patience, but it can certainly be done.
Many of our original Satins were jumpy and aggressive, had litters of 6-8, with some of the bunnies having tendencies to weaning enteritis and nest box eye, took 12-16 weeks to reach 4-5 lbs, and the does were pretty much done producing by their third year. Granted, it's been 13 years, but our rabbits now produce huge litters (10-16 kits) for about two years, are able to raise most or all of them (I do foster out some bunnies from the litters of 12-16), continue producing litters of 6-8 kits into their 4th year, and have health problems very rarely or not at all. The growouts make fryer weight by 8-9 weeks. In addition, our rabbits have extremely good temperaments, also a result of selection. In fact that is what I prioritized first, and is my only non-negotiable requirement. A calm, gentle rabbit will also be healthier and grow better than a psycho scared rabbit; plus, I am not willing to deal with a rabbit that attacks me no matter how pretty she is!
