Lets play devils advocate:
It all depends on what you bring to the table for your employer. If your day to day tasks do not change after you get the PE, why should they pay you more? I understand you may be worth more to a new employer, but I dont think company A should pay you more just because company B will, especially if you dont bring anything new to the table.
If you want a raise from your current employer, make yourself more valuable. Take on the responsibility of being a design lead, project manager, take a more involved role with the company. Adding 2 letters to your name is worthless if you just stay a CAD-monkey.
Also, is a PE necessary in your line of work? Some industries and employers dont want and/or require a PE. Look at construction, despite needing a civil degree to get some of the jobs, you are not needed to get your PE to get promoted to superintendent or higher. My first employer (heavy highway contractor) actually discouraged engineers from getting their PE, because it would mean they would leave since the contractor let it be known they wouldnt give pay raises.
Also, what it the current state of your employer and industry? If you work for a land development consultant right now, they may be doing everything they can just to not crash. If there has been a 2+ year pay/hire freeze, how do you think the other employees would feel if you're demanding 10% or more without doing anything new for them?
The company i worked for when i got my PE wasnt able to give an immediate raise because the projects i was working on had me at a contracted EIT rate. My responsibilities didnt change, my company wasnt billing me out for any more, and was actually losing money because they had to add me to their liability insurance. When i talked with my boss after passing, he explained all of this to me and let me know that as soon as we started on a new project i would get a raise (10% raise received 3 months later).
My point: look at the whole picture before you trash your current employer. If after that you still want more (both more $ amd more responsibility), then talk with your boss and explain yourself.