Yes and no.
There are some jobs (most often very specific government jobs and military) that require citizenship for security purposes. When it comes to these jobs, the citizen will qualify and the PR won't.
For all other jobs (i.e. the vast majority) a PR and citizen should have the same shot. I have certainly never differentiated in my hiring. In fact, I don't even know if the person I'm interviewing is a PR or citizen.
The only exception I can think of is some consultant roles. For some consultant roles you are required to travel frequently and with little notice. For these types of jobs I have heard of situations where PRs are not hired if the come from certain non-visa exempt countries. This is because they must apply for a visa if they want to travel on business to the US, EU, etc. and this takes too long / there is no guarantee the visa will be approved.
