SSDI is an administrative process, that, with all its flaws, is not adversarial.
You file your claim and the SS staff makes its determination. If your claim is denied, you can ask for reconsideration. (One tip -- it is often very smart to retain an SSI/SSD lawyer to assist you -- the fee would be on an hourly basis -- and help prepare your request for reconsideration as that dramatically increases your chances of victory on reconsideration.)
If you are denied then, the SSD lawyer appeals for you before an administrative law judge and as a fee, gets up to 25% of your back benefits but not more than $4,000. The test is not mere disability, but the inability to hold any job that is present in reasonable numbers in the US economy. So if you were a brain surgeon who got carpal tunnel and can't cut, there are lots of other things you could do not, including act as a secured access lot gatekeeper. That would deny you SSD.
On disability insurance the fact that you qualified for SSD is often influential, but not binding.
As to whether or not it pays to sue, much depends on whether the plan is one provided by your employer or one you purchased personally. If the latter, a company that denies in bad faith can be liable for punitive damages. But if you have to sue, that is often very costly as the insurance company will defend vigorously. My suggestion is that you should get an expert in the field -- either an SSD lawyer or an insurance lawyer -- to help you prepare your application to the insurance company too. What is often crucial is demonstarting your disability and an inability to work.
