This is going to be long. Sorry.
Both pedigree dogs and crosses can have issues.
With ANY puppy, you need to ask if the breeder is testing for widespread issues like hip dysplasia. If not, why not?
You also need to know why the litter was being bred. To produce working dogs? From dogs of good temperament and sound conformation who will mostly be pets? To produce a show prospect? Or just two dogs being glued together for the £££?
What are the parent dogs like? Do you have a pair of nice chilled-out show-line labradors? Or a neurotic Malinois who takes that breed's inbred urge to bite to extremes being crossed with a physical shambles of a GSD? Or two hyper cocker spaniels?
How are the puppies being brought up? Lots of exposure to new things? Being handled by several different people or shut in a run in a pokey barn with their dam?
Pedigree dogs can have issues due to a narrow gene pool. Think of it like this. Dog A is an excellent example of his breed and is used multiple times to produce puppies. He produces some excellent progeny, several of whom are, like him, studded out multiple times. Within a couple of decades, there are very few lines of the breed that don't carry his genetics.
There's a problem, though. Dog A carried a nasty recessive gene. No a problem if the dog only gets one copy, horrible illness if it gets two. Hence issues like Collie Eye Anomaly. Vizsla polymyopathy is another one that is almost certainly caused by a recessive gene, but as yet there is no test for it. As a breed, they went through a very tight bottleneck post World War II, so it might be due to that rather than the overuse of a particular sire and his progeny.
Sometimes this narrowing of the gene pool happens much more slowly and less obviously, but it's why some genetic tests are recommended for some breeds and not others.
And the other issue with some pedigrees is their morphology - long backs prone to disc issues, flat faces so the dog can't breathe properly etc.
Cross-bred puppies, however will still need to come from tested stock if both parent breeds carry the same recessive issue (for example, the same form of PRA). And the chances are much much higher that they are being churned out purely for the £££, and will come from a puppy farm which is NOT the best start in life.
It's lot harder to find a well-bred cross than it is a well-bred pedigree. And some things will come down to your personal preference. Are you okay with the sire not having had his hips tested but instead being in work aged 10? Would you be happy with a random farm-bred non-KC Jack Russell, brought up in the farm kitchen and around the yards, who is confident with all sorts of people (noisy men in hi-viz, squealing grandchildren) and loud machinery and lowing cattle, because at least one of them will be staying put to help its mother keep the rats down? Or would you want a Westie from fully health-tested stock nurtured in the breeder'
s calm suburban house and garden? Me, I'd go for the JRT, because as a type they're as tough as old boots and I like a drivey dog, and Westies tend to bark a lot and have skin issues, but you might see things differently.
There are no guarantees. All you can do is to shorten the odds for you and the puppy to what you consider acceptable.
And above all, consider what it is you're getting. A Malinois is not a German pointer is not a pug is not a border terrier. Working lines and show lines are very different things.