Disclaimer - we own the grey car that is for sale on TradeMe.
The Baur conversions were originally produced because BMW didn't have a convertible in their range. Coupe bodies were shipped from BMW manufacturing plants to the Baur Karosserie facility in either Germany or south Africa (depending original location of manufacture). There were slight differences in process - German cars were rust protected and suchlike before being shipped, were then modified and painted. SA cars were shipped in white, modified, then rust protected and similar.
Baur are an extremely highly regarded organisation. Aside from work they have done - and do - with BMW (starting in the 1930s, and more recently on the 2002, E21, E30, E36, E46 conversions and others) they also did all the bodywork for the Porsche 959, conversions for Opel and Mercedes, and do prototype work for VAG and Ford.
The Baur design for the E30 means the car uses coupe panels and parts (other than the roof). The convertibles BMW produced later use different body panels. The Baur retains the 3 seats in the rear (presumably for small people!) while the convertible has two seats.
The Baur roof design means the structural strength of the coupe is retained, and offers several positions.
Another benefit of the Baur is that the roof does not leak. My wife and I know this from experience - driving from wellington to Waikato we encountered a storm that meant we had to pull over - it was impossible to see the road. Not one drop of water got into the car.
They're not to everyone's taste, but are extremely versatile and easy to look after.