These two share something else: they involve a little sleight-of-hand by their respective makers. Everything you can see and touch in the A1 is Audi-specific, but underneath it's a Volkswagen Polo.
As you've already read here, the 4008 is a revamped Mitsubishi ASX: most of the exterior panels are different, but the interior (bar a couple of detail changes) is the same as the Japanese donor car.
The question is: which reboot provides the most convincing compact-premium car? On the surface, I'd have to say with Peugeot walks away with the styling prize. It looks gorgeous and beautifully proportioned, whereas if you look past the four-ringed badge the Audi appears a little awkward.
This pair take different powertrain routes. The A1 is classic VW Group stuff: a small-capacity 1.4-litre turbo engine making big numbers (90kW/200Nm), matched to a high-energy dual-clutch seven-speed automated gearbox.
The 4008 picks up Mitsubishi's 2.0-litre engine (110kW/197Nm), with a continuously variable transmission (CVT). The Audi is a smaller, lighter car: under 4m in length in fact (Peugeot is 4340mm). So it has more performance zing, achieving 0-100 km/h in just 9.0 seconds compared with the Peugeot's 10.2 seconds. It's a lot more thrifty, too: on our real-world open-road test route the A1 returned 8.9 litres per 100km, against the 4008's 11.2l (the official figures are 5.3/7.9l).
Not all of that difference is down to size. The A1's powertrain has more character and responsiveness, so you tend to engage with it more. It's really good fun, whereas the 4008's petrol mill is noisy and poorly served by the "gearless" CVT, so you tend to just plant the throttle to the floor for meaningful forward progress. Both cars have paddle shifts as standard; the difference is that you don't often feel like using them in the 4008.
The 4008's steering has better feel and it corners with assurance thanks to a wider track than the ASX. The Audi's chassis is aloof, but it's easier to place on the road because it's a smaller car. The 4008 has the edge on ride, though.
Inside, it's no contest on quality: the A1 has a stunning cabin, full of soft-touch materials and ergonomic good sense. The only disappointment is the pop-up information screen, which looks high-tech but is pretty pointless without sat-nav (a $3800 option). The 4008 does not disappoint; the Mitsubishi donor car is nicely configured and Peugeot has added a new instrument binnacle finish. But it employs clearly cheaper materials and doesn't give the same impression of premium motoring.
The Peugeot is bigger by far, however, and better equipped. An extra 201mm in the wheelbase means much more room for passengers and cargo, although the Audi can still accommodate adults in the back - with a few packaging tricks, such as a rear-seat squab that's angled sharply downwards.
The A1 is hardly sparse, but it cannot match the 4008 Allure's automatic air conditioning, cruise control, rear parking radar and 18-inch alloys. To add those items to the Audi would add another $5420 to the price.
Verdict? The Peugeot just looks so good. In terms of style and value, it could almost take this contest - if it didn't have a disappointing engine and the dreaded CVT gearbox, which is death to driving pleasure.
The Peugeot looks good, but the Audi feels good in every possible way. It wins.
The bottom line
Peugeot 4008 almost gets there on style and space, but Audi A1 wins with quality and driving pleasure. Me? I'd spend $37,900 on a Volkswagen Polo GTI ...
