First up, I'm clearing my stand: I am against competition. Any form- formal, informal, etc.
Now,
I saw some people talk about Racing and how it has brought better tech into everyday cars. But have you noticed that only those areas have developed (at a fast rate) that actually use elements used in racing- like speed, braking, balance, agility, etc.
But the other factors that we common car-users need haven't developed that well because they aren't used in racing. Examples- Technology that makes it easier to park cars, fuel efficiency, lesser polluting cars, etc.
Thus my point: competition does help, but only to improve in certain areas that is demanded by the competition and not overall. That's why sharks and lions are better hunters (as M2 mentioned) than humans, but hunting is the only thing they can do. But primates have been known to work cooperatively. Result: They evolved into homo-sapiens (humans), and are doing way better in this planet than the competitive Lion/shark.
Of course, this are just my opinions, stated with all due respect to people with other opinions.