Depends. If you're a talented engineer you stand to make a lot more money as a contractor if you stay busy and set your rates appropriately. The average salary in my area is $140k for a senior software engineer. As a contractor I could make $110-150/hr which could be $170k at the low end once the extra taxes paid by contractors are taken into account. None of those numbers include normal state and federal income taxes which would apply equally to both. Also being a corp entitles you to play a few tax games which let you reduce your tax burden slightly.
I was contractor for a while and never saw those $100-150/hr contracts. In my current company the contracting agency gets within that range but the contractors themselves see much less.
It helps to form your own corp and go direct. If your company can charge $150 for you, then you have a chance at charging $150 for you. Your company might provide some added value, so you might need to drop your rate a bit, but if you develop customer relationships and consistently meet expectations then you can get away with jacking up your rate a bit. There are times when you still might have to take a lower paying job but it varies.