The 630 CS used a 2986 cc I6 M30 engine with a Solex 4A1 carburetor, making 184 hp (137 kW) at 5800 RPM. The 633 CSi used the same engine, but with a Bosch Motronic fuel injection system, which increased output to 200 hp (150 kW).
In 1983 BMW took the M88/3, a modified version of the M88/1 from the BMW M1 and put it in the E24 chassis, creating the M635CSi, the US variant of which was called the M6. The M6 also had improved suspension, brakes, and a close-ratio manual transmission
My personal opinion is that the E24 6 series remains a desirable and livable car even today. However, these are now nearly 30 years old in many cases and great care must be taken when looking to buy one. These cars are prone to rusting in hidden areas. I highly recommend using the European Car Magazine E24 6 Series buyer's guide to help inform your decision.
The E24 design is still held by many BMW purists as the pinnacle of 'big coupe' design, and it was certainly never equalled aesthetically by the antiseptic 8 series, a coupe one journalist described as "a complex, heavy, soul-less touring car for the moneyed."
If it were my wallet, I would look for a european-spec (ie 'grey market') 1978-1983 635csi. These had none of the horsepower robbing smog equipment, the full 3.5 liter displacement, and over 40 more hp in stock form. They are also 400 lbs lighter than their US spec 633csi/635csi cousins, lacking the huge ugly bumpers. A few mild mods really wake these cars up. If your bankbook says go for it, though, the euro M635csi and US M6 are truly matched only by the great Porsche 911SC and Carrera 3.2 for timeless looks, performance, and reliability. The buyer's guide in European Car magazine (link above), is a must-read for more detailed technical information on the differences in these cars.