Both. All dogs can be prey or predator, depending on the circumstances. Dogs may try to catch insects, mice, or other small animals. If so, they are acting like predators. A poodle could be prey for an alligator, an eagle, a fox, another dog, or a coyote, and possibly other large animals. When one of these predators is trying to get the poodle, it may fight back or run away.
Some dogs are more likely to act as predators than others depending on what they have been bred for. Size is somewhat of an indication as to how much of a predator instinct a dog has, but isn't definitive. For example, Terriers come in all sizes, from 7 pound Yorkies to 50+ pound Airedale Terriers, but they are all bred especially to hunt and are all have strong predator instincts.
You don't say what kind of poodle. Standard Poodles are the largest of the poodles. They are 15 inches or taller as adults measured from the ground to the shoulder. Adult Miniature poodles are 11 to 15 inches and toy poodles are under 11 inches in height. Teacup poodles are even smaller.
Standard Poodles were bred to be companion hunting dogs, like retrievers. They have to have what are called "soft mouths" - so as not to damage the bird or game they are retrieving; they have to be gentle. They were also bred to be comfortable with other dogs around and with loud noises like guns firing, strangers being around, and crowds. So, most standard poodles don't have strong predator instincts. However, because of their size, they aren't typically prey. When a smaller dog, animal or child runs away from a dog it may set of their predatory instincts.
That being said, any dog's predator instinct may be set off by these cues - seeing something fleeing. If you do an internet search for "poodle attack" you will find instances of poodles attacking other dogs and children.
A standard poodle is less likely to run away than a miniature or smaller poodle when attacked. Still, I find that smaller dogs are sometimes more reactive because they do have the possibility of becoming someone else's prey. They may be so defensive that they go on the attack. That isn't really predatory behavior because it isn't a chasing instinct. As I said however, any dog can have its predatory instincts set off.
There isn't really a category or instinct for a prey animal. Being prey is just being on the receiving end of another animal's predatory behavior.