To my knowledge -- keeping in mind this is not my area -- there are modest benefits for newer types of insulin. You have to dose less often. The variance in swings of blood glucose is lower -- newer types tend to be more "extended release". Some types can be inhaled instead of being injected, which is obviously preferable.
But in my understanding, in general, there are no major health risks from using plain insulin, and it is mostly about convenience. I do not know if that is true for all diabetics.
EDIT: kkreamer above says there are differences in long-term complication risks between insulin types. From my very brief literature review just now, that looks to be true. I guess I have become jaded because of the number of diabetics I have recently heard complaining that they are in danger of IMMINENT DEATH because they cannot afford their insulin. Long-term complication risks are important but it is not the same thing.
This is how pharma keeps the whole scheme going. They invent a drug that is marginally better in some way, refreshing the patent. Then, if the consumer cannot afford the product that is even 5% better, the consumer feels as if they might as well have been sent to a death panel.