Funny, I was looking into this a short while ago (laminova oil coolers).
Main advantage is it will heat your oil quicker, which can be a problem especially in winter. It can take a long time of driving to warm up the oil... especially when running in a 50 second hillclimb event.
Modern oils are better true, but the thicker the oil the more the oil pump has to work to move it around. Minis run a thicker oil than most other cars, as the gearbox oil = engine oil.
Unfortunately, for $700+ for the S34 model and then AN fittings, it's just not worth it... oh and these coolers RELY on the water temperature being less than 80-90 degrees to cool the oil... as you imagine the hotter the coolant temperature, the less effect the oil cooler
has. As dr mini pointed out... why tax your cooling system more. Also, if your engine overheats a little [eg 90 - 95 degrees], it will throw up your oil temperature (you wouldn't even know!)... not good to build systems with these kinds of dependencies.
Have a look at their performance graphs and even at 80 litres/min they don't cool any amazing amount...
Just stick to the good ol' MOCAL 13 row at the grill

Tried and tested with 30 years of motor racing. Most road cars don't need an oil cooler. How would you know? After running the car on the highway until your water temp peaks, stick a thermometer down into your dipstick hole.