As for the quality, nothing that proper capture sharpening can't address.
Before I give my two cents, I'm going to have to disagree with the above statement. If your lens has image quality issues that result in any amount of detail being lost, there is nothing you can to do get that detail back (unless it's out of focus, in which case you can salvage some detail, but not get a perfect image back).
That said, my two cents:
I think there's a trade-off to be had here. I don't know how critical size is to you, and obviously you can decide on that pretty easily. The rest of the trade-off has to do with the sort of things you take pictures of, and the conditions under which you do so.
A lot of people have stated that IS is no substitute for real stops, and they're right. What a lot of people haven't said (from what I've seen), is that real stops are not a substitute for IS, either. That said, I find I do care about real stops more often than I care about IS, but that probably doesn't apply to everyone (although... who in their right mind shoots landscapes without a tripod, anyways?).
With that in mind, and your budget considerations, I would suggest having a good solid look at the 70-200/4L, including the following major differences:
-less than half the price of the DO
-not as long at the long end
-a stop faster (As someone who's bought f/5.6 lenses before, I take this one pretty seriously. Never again, for what I do at least.) This can also present itself as an issue when autofocus speed is critical -- faster lenses, as a general rule, autofocus faster, especially when you're approaching the minimum aperture at which your camera body will autofocus.
-if there was an IS version of said lens, it would be an even easier decision, but alas it doesn't have IS, so if you need depth of field in reduced lighting conditions, that's a big consideration
-size/weight: the 70-200 is definitely a physically longer lens, but it's actually lighter by just a hair (15 grams IIRC), so if size doesn't mean the end of the world for you, it's a convenient lens to carry around
-funny artifacts from DO zoom(s)
I don't presently own either of these lenses, and I don't particularly plan to, although I might be getting a 70-200/4L for someone as a gift some time soon (no, not you ;). If I were getting one, though, the big deciding factors would be speed (aperture) and image quality. Oh, and there's also the 70-300 IS USM that came out recently, but that also suffers from weird pictures (coloured bokeh), IIRC.
Oh, and no, Sigma doesn't make any IS lenses last I checked.