No. Purebred cats are not "better" cats by any measure. We can get a mixed breed cat who is as smart, affectionate, healthy, and well-behaved as a purebred cat.
Because these things depend on the individual cat and how they are raised.
That's the short answer. The long answer is what "purebred" means.
The purebred cat comes with papers saying they are a certain breed, and so were their parents, and so were their parents, as far back as the "breed standard" goes.
Which can be as far back as the dawn of time or as recent as a decade ago. The Cat Fancy organization has certain rules about what makes a breed, and then it's a breed.
That's what it means. And that's all it means.
Here are the plusses, and pitfalls, of getting a purebred cat.
The good news:
What purebreds offer is predictability. If we want a devoted, talkative, and active cat with a long, lean body and a face, feet, and tail of a lovely contrasting color, we can get a Siamese kitten, and know it will grow into a Siamese cat. If you grew up with a Siamese and adored him or her, your chances of getting a similar cat is greatly increased by getting another Siamese.
This is how breeds of cats get their fans. People know they can get more of their favorite kind of cat. They also know if they want more than one cat, the chances of the cats getting along are increased if they are the same kind; with the same traits and preferences.
Or maybe you are allergic, and need to get a cat known to be less likely to trigger allergies, such as a Sphinx, Cornish Rex, or Siberian. That's also a good reason to get a purebred cat.
An ethical breeder will provide prenatal care to their mother cats, and raise the kittens "underfoot," with good socialization and other early training. This can be important to people who don't know how they would handle a cat with an uncertain past.
There's certainly nothing wrong with wanting, or getting, a purebred cat. As long as you avoid the Purebred Picking Mistakes.
The bad news:
There is no shopping for bargains with purebred cats. Many people look into a certain breed, then draw back with "sticker shock" over the price tag. Then they discover they can get the same breed from someone else for half that price. Doesn't that mean they found a great deal?
I'm afraid not. There's a better than 90% chance you have actually overpaid for a living nightmare.
The very point of a purebred cat is a restricted gene pool. You want a Norwegian Forest Cat or a Chantilly/Tiffany, and you get it; that's not the problem. But to keep such a restricted gene pool producing healthy cats, good breeders need to match their father and mother cats carefully, and monitor any bad recessive traits with medical testing. They will take problematic cats out of their breeding program. They don't sell sick, or potentially sick, kittens.
That's expensive. That's why the kittens are expensive.
Bargain breeders don't do any of that. So getting a "bargain purebred" usually means getting a kitten whose mother didn't get those prenatal checkups, whose father might be carrying a tendency to heart trouble, blindness, or blazing skin problems, and whose early life was spent in a box in the backyard to be whisked onto the market too early so the seller can take advantage of tiny kitten cuteness.
It means falling in love with a kitten who will cost their low price over and over again with vet bills until their too-early death.
Or it means not falling in love at all; bad breeding can produce a kitten who spends their life hiding under the sofa, screeching at all hours, or fighting with everything that lives and breathes.
If you've ever heard someone remark, "Oh yeah, that breed. My mom/uncle/best friend had one, and it was a horrible cat," you are hearing about a bargain breed purchase.
Horrible cats don't have fans. For good reason. But it's not the fault of the breed. It's the fault of someone who didn't know how important it is to pay full freight on a purebred kitten.
So, how do you get your dream cat?
If you meet a friend's cat and find them adorable and gorgeous, if you read up on a breed and discover qualities that sound incredibly attractive, or if you have allergies or other life style restrictions that mean you need a certain kind of cat, you still have choices.
Just make the right choices.
Here's the right way to save money on purebreds.