If you have a choice between the new government health insurance and private, which are you going to choose?

How will it effect private insurance? Will a lot of employers drop their plans, hoping that the government will cover everybody now?
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Simple economics. The tax imposed on employers for not covering their employees is less than the cost of providing insurance, which will cause many employers to drop the plan, especially if the economy is bad when the bill becomes effective. Some employers will "carve out" management and offer them private group coverage and let the regular employees fend for themselves. There will also still be private group plans for union workers because the unions will demand the superior coverage. Of course, government workers will still have private coverage. Current private individual plans will vanish because they will not be allowed to add new members. Through attrition the plan membership will become so small that it will not be economically feasible to continue the plans. Private companies that offer exchange qualified plans will be available but the cost will be much higher. This is because the government option uses Medicare doctors and pays the doctors and hospitals Medicare rates plus 5%, which is 50% to 70% of what private companies pay.
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