The general reason an F2 cockapoo is better than an F1 cockapoo (and an F3 cockapoo is better than an F2 cockapoo, and so on) is because of the likelihood of consistent cockapoo characteristics.
An F1 cockapoo can not be a "cockapoo" at all. It can really be a cocker spaniel mutt. Or it can be a poodle mutt. Or it can actually fall in the middle, and be a cockapoo. This makes getting an F1 cockapoo a game of Puppy Roulette. You have to have a very experienced eye and a good breeder, willing to work with you, to get a dog that is an actual cockapoo (or in your case, perhaps leaning towards the poodle side of the family). The further down the line (provided the parents of the puppies are actual up-to-standard cockapoos) the more likely it is that all (at least most) of the puppies will be actual cockapoos.
An F1b dog would be a cockapoo bred to a toy poodle. This would probably yield a much smaller dog, since a toy poodle is under 10 pounds (to be considered a toy). If bred to a miniature poodle (& not a "toy") then it might not shrink the cockapoo's size too much. Size of the dog is more important than people realize!
This F1b dog would not be considered a cockapoo by any real breeder. I don't know what that is called... but the cockapoo breed has been around since the 1950s and has a few clubs and a basic set of standards that breeders agree with. An F1b dog would be (roughly) 3/4 poodle and 1/4 cocker... it is pretty much a "poodle mix" or a "poodle mutt".
I personally would not like that cross. You might as well just get a poodle (from a reputable breeder of champs-so health is assured) if you're going that way. I really like the characteristics that the cocker brings to the cockapoo. With an F1b you lose the "hybrid vigor" that accompanies the crosses, and any breeders making these dogs are almost guaranteed to be jerks breeding from low, poor-quality breeding stock!
The ONLY reason (that I have ever heard of) for anyone to breed F1 cockapoos is greediness. They do not produce consistent, reliable puppies.
A side note... why did I say try not to trust designer or hybrid poodle or doodle or yorkie mixes? Well, this is because most breeders are greedy and so they breed first generation crosses.
So why would breeders breed first generation crosses if they KNOW that the absolute best reasons for crossing these two is to give the sweet, loving and docile nature of the American cocker spaniel the intelligence and excitement of a poodle (while not being high strung like a poodle) and the best of the best? THEY DON'T SHED and they are LOW dander....
So what gives? Well, these greedy breeders like to breed their large female Cocker Spaniels (35-45 pounds) to their tiny toy poodles (a toy must be under 10 pounds to classify). This can give puppies that are 45 pounds at adulthood or 10 pounds at adulthood! Or anywhere in between, and no matter what any breeder says you can NOT tell how big a dog will be from birth without it being a very very very rough estimate. Even with experience I can personally only claim knowledge of small or large size on 2-3 pups per litter. The rest are generally "average" beacause I cross F2 dogs. My sire and dam are both gorgeous, accepted standard and perfect Cockapoos, so most of their babies are as well.
Also, when a dog-breeding business has both cockers and poodles they can breed three different kinds of dogs, instead of focusing on one (and appeal to a broader client base). It also helps the breeder choose new breeding stock a LOT easier. When you are choosing a cockapoo for breeding stock you have to really pay a lot of attention and pick carefully, and you could end up with a sweet dog that you cannot breed because he/she do not possess the proper traits. For many breeders, this is just a business and nothing more. All they are interested in are the best business decisions and their livestock hardly matter (or the happiness of their families too).
Many F1 cockapoo breeders also use their poodle to create other popular designer hybrid mutts, which are gaining popularity these days. A sign of a breeder to stay away from is anyone that has more than 2 breeds of dogs that they breed! There is no way to be an absolute expert on several breeds and there is no way to give multiple litters the individual training and attention that they need.
Even with our F1 cockapoo parents, every now and then they throw a smooth-coated cocker-looking puppy that doesn't have fur, but tends to lose hair more frequently and in slightly more abundance. If you would go with any "doodle or poodle" mix you need to go deeper in generation, the more the better! (It will take me some years of acquiring good stock and investing time into having the ideal, ideal F4 puppies! and since I don't charge very much for my puppies, it will take a little extra time for me :-)