It depends what EE you did. There are different kind of jobs in EE. Some of them can't be out source, such as utility company. Software job is, normally, going with projects, I mean, projects are performed one by one, and company by company. Yes, there are a lot projects, but they may not be in one company all the time.
So make your decision by your situation.
By the way, I did software before and now I am electrical engineer. I hope to be stable and don't worry about to find jobs every a couple of years, in my situation.
Good luck.