Both sauces are delicious, but they are definitely very different in taste and texture. After spending probably too much time thinking about them both, I realized that Rao's sauce reminds me more of a classic red-sauce joint, while Carbone's sauce transports me to a fancy pasta restaurant.
I take my pantry staples seriously, and I need items that are versatile but also reliable. I keep a jar of sauce on hand for things like last-minute pasta nights, but also for fortifying beef stews, making Sunday gravy, and salvaging vegetables that are close to going bad.
The Carbone sauce I tried would not fit those needs. It's too distinct in its flavor, in my opinion. Rao's sauce, however, is more malleable, takes on other flavors well, and boils down nicely. I wouldn't want to alter the Carbone sauce like that.
While I feel Rao's is ready to go at room temperature, I wouldn't dip a mozzarella stick into the jar from Carbone. So if you're looking for an all-purpose sauce to keep in your kitchen, I'd recommend purchasing Rao's. But if you're buying jarred sauce for a pasta recipe or to make a dish like Carbone's meatballs, I'd recommend trying his namesake sauce.