IMHO:
Shutters: Both are very reliable if used frecuently. They strongly dislike to be letf unused for long periods of time. The one in the II/III is easier to repair.
RF: The one in the II/III is not only longer-based, but it is a completely different mechanism that is almost imposible to get unadjusted. The one in the IIIa is more pedestrian.
Size: The IIa is quite a bit smaller. A significant difference, again IMHO.
Lenses: As above, the pre war Biogon and its soviet copies do not fit the IIa/IIIa. Of course, there is always the magnificent post war Biogon, but at more $s. If the bodies you are contemplating come with their original lenses, the one in the IIa is probably coated and the one in the II is probably not.
And... Meter: I strongly favor having an inboard meter. If working right, the meter in the Contax IIIa is an useful tool, not a gimmick. I use mine in all but the lowest light levels, and it has never failed me. Of course, it adds nothing to the camera's aesthetics.
All that said, I do use a IIIa as my daily camera, and wouldn't trade it for anything. I like its size, its controls are second nature to me, and even although I had the luck to find a very cheap post war 35mm Biogon, I never use that focal lenght. Its RF is accurate enough to focus the 135mm wide open, which is all I ask form a rangefinder. Its 50/1.5 Sonnar and 21mm Biogon are hands down my favourite lenses. And I've been using it for over 30 years, which helps a little ;-)