This review claims the new f/2 is sharper:The Digital Picture 200mm f/2 L IS USM Lens Review
From the review:The Canon EF 200mm f/1.8 USM Lens was long-discontinued (due to lead in the manufacturing process) when the Canon EF 200mm f/2.0 L IS USM Lens was announced. The 200 f/1.8 was one of the few discontinued lenses that I purchased simply to evaluate for this site - it is legendary. Unfortunately for my credit line, I bought it before the 200 f/2 L was announced and sold it before the 200 f/2.0 L price was established. So, I don't have the 200 f/1.8 in front of me for a direct hands-on comparison. I found the 200 f/1.8 to be a sharp lens, but not as sharp as the 200 f/2.0 L wide open. The 200mm f/1.8 L has less-advanced focus-by-wire electronic manual focusing and did not yield the AI Servo autofocus hit-rate that the 200 f/2 is delivering for me. The 200 f/1.8 was not as comfortable for me to hold and shoot with (I found it to be front-heavy), and I did not care for the tripod ring location. The 200mm f/2.0 L focuses closer (6.2'/1.9m vs. 8.2'/2.5m) and has 4-stop IS. The 200mm f/1.8 has a 1/3-stop wider aperture. Canon no longer services the 200 f/1.8.
I sold my 200/1.8L after learning that the 200/2 will be out and before picking up the new 200/2L IS. I cannot compare it side to side but I am quite happy with the 200/1.8L but do miss the IS function, which was why I sold it. The 200/2L IS is just as fantastic, if not better. I usually shot at f/4 or smaller, the advantage of extra bight lens for me was more precise focus, and faster focus, and 200/2L IS is to me at least as good in sharpness, and a lot more helpful with the IS and I believe better constructed.