I am blessed to be gainfully employed by a large fortune 500 company and have been approached by a small company in the private sector with a compelling offer that I would like to accept.
I notified my employer of my intent to leave, who asked me to pause while they assemble a counter-offer.
The small company package is 20% more valuable than my current wage. The large company plans to counter with a package 30% greater than my current wage.
After I receive the counter offer, is it courteous/acceptable to approach the smaller company and ask them to match the larger offer? If so, is it unprofessional to ask both parties for a best-and-final offer?
In the event I accept the smaller company's offer, the large company asked that I consider contracting my services for 6-12 months after my departure, nights and weekends. Is this common? The companies are in different industries and are not competitors.
Update: 2016-02-09, copied from comments
A lot has happened since then, but long story short I gave 30 days notice and went with the private sector offer. It turned out to be the best decision I ever made; the private sector was a better personality fit and gave me room to really innovate/excel. I've since been promoted to senior management and my standard of living largely exceeds what the counter-offer in the original post would have provided. Not for everyone, but def would not have happened if I stayed at the big public company.