I don't have a Leica IIIb, but compared to the IIIc & IIIg, the Reid III is certainly as well-built if not better. IIRC, in my discussions w/Don Goldberg ("DAG"), who got 1 of mine into working condition, he said that many, if not most, of the Reid & Sigrist parts are not interchangeable w/Leica because they are smaller & made to tighter tolerances.
As far as the Taylor-Hobson 2"/2 Anastigmat, I would mostly agree w/Mr. Hicks that it's comparable to the collapsible Summicron, but more flare-resistant (in my experience, anyway) perhaps because of better coatings. I've never used a Summitar, so have no basis for comparison there.