It depends on which field you are referring to. There are many types of doctorates. As far as medical doctors are concerned, admission to medical schools is extremely competitive.

it means you are falling behind and your employer probably see's your lack of effort and healthy competitive behavior

Even though the pediatrician field can be somewhat competitive when it comes to finding a good position, there is still an ongoing need for pediatricians. The reason for this is that babies continue to be born regardless of the economic climate.

That sort of depends on what you mean by competitive. People compete for money to do paleontology, but it isn't as cut-throat as biology. Generally there are so few paleontologists that it is easy to know everyone in the field. It is a good field for hard workers.

It doesn't look like the schools themselves are competitive, but the field itself is, so take that into account if you want to apply at a school.