I own a 1956 BMW Isetta, a 1962 Austin Mini, a 1966 Austin Mini-Cooper 1275S, a 1967 Saab 96 2-stroke, and a 1973 Saab 96 V-4.
The mechanical layout of the smart is closest to that of the Isetta, with the engine and transmission at the rear (engine somewhat to the right, if one is facing forward, and the transmission somewhat to the left). While the geometry of the smart is similar to that of the original Mini, the handling and driving experience are entirely different. The standard Mini-Cooper 1275S has about the same horsepower as the smart, but is six hundred pounds lighter, so is quicker (my Mini-Cooper has racing modifications and is considerably faster). An original Mini-Cooper, when driven by an expert, will still out-handle most cars of any kind on small roads, though the smart is delightfully sporty while being vastly more comfortable and luxurious.
Of my vintage micro and mini cars, and others I have driven, the smart driving experience most closely resembles that of the Saab 96, an extremely solid and refined motor-car, especially for its size. The power and weight of the smart are almost identical to those of the Saab 96 V-4, with consequently very similar performance. The high, upright seating position of the smart is also very reminiscent of the Saab.
Overall, however, the smart is wonderfully unique and not directly comparable to any of the vintage motor-cars under discussion.