Here's some more thoughts.
As mentioned, canon won't work on these any more, as they have no parts. Some 3rd parties can and do still work on them, and have a parts stash, but it can be hit or miss. If the AF dies, the whole lens is basically useless since it's drive-by-wire focus. Other things that annoy me about the 200/1.8: overpriced, even now. If it was <$2k, I'd say take the chance but at $3500+ it's not worth it, even if it was better optically (it's not). Also, it's very front-heavy. When hand-holding, this is a pain. the 200/2 is better balanced. The hood for the 200/1.8 is huge, and doesnt' store reversed on the lens without a 3rd party lens foot (RRS, et al.). Speaking of that hood, don't break or lose it, as replacements are impossible to find and $500+ when one does show up, it seems.
Many of these 200/1.8s were used by pros back in the day and got pretty beat. They were expensive when contemporary (mid-1990s), and somewhat under-loved at the time (sort of like the 50/1.0L was un-loved back then). Of course when discontinued, the value shot up and has remained high ever since.
Re: 200/2 - the IS is worth at least 3-4 stops, which is ok as long as your subject has little motion. Frankly, I think the bokeh from both of them is great, but that's a subjective topic so it's hard to say if one may be regarded as better.
I think the IS, plus weight balance, size, servicability, and optical superiority (in every measureable way, basically) puts the 200/2 as the better choice. The only downside is price. the 200/2 is not cheap. If a 200/1.8 could be sourced for $2k or less, that's about the break-even point in my mind with regards to risk vs. quality/usability vs. cost.
Olympus also made a 180/2 for the OM system but both Canon 200s are significantly superior. If you can live with 2.8, the EF 200/2.8L is a great lens and a serious steal, price-wise vs. the 200/2 or 1.8.