Engine technician here. Expanding on what has already been posted...

The only reason that diesels have a reputation for long life (durability, not the same as reliability) is because traditionally those diesel engine blocks were built very strong to deal with the high peak cylinder pressures required for the compression-ignition cycle. If two identical engine blocks are available as diesel and spark-ignited versions, the spark-ignited version lasts much longer, all other things being equal (but they usually aren't actually equal). The parts that last longer are the cylinder bores, and the crankshaft. A good example would be the spark-ignited natural gas industrial engines built by Caterpillar, which started out as diesels, and which are so under-stressed that they run for a very long time between overhauls, even longer than their diesel equivalents.

An automotive-duty diesel will not last longer, as it is typically designed to the same service or duty cycle as the gasoline equivalent. Reference the VW diesel Rabbit as an example. Old Mercedes diesel taxis lasted a long time (built like boat anchors) but then so did the gasoline equivalents (also built like boat anchors) BMW is using a different block design for diesels than gasoline engines, built to withstand the high cylinder pressures, but expecting it to run longer than the gasoline equivalent is misguided. It shouldn't last any less time. Now, since this is all theoretical, does it really matter? You are very unlikely to trade in either model because the cylinder bores are worn, the electrics will sideline you long before that. Even better, wait and see how the higher diesel torque helps the automatic transmissions last longer, lol.

Turbocharging isn't a determining factor in the wear equation, power output is. You can get that power through NA or turbo means, but I wouldn't expect turbocharging to have any impact on durability.

Now consider reliability, a totally different concept. This isn't about how long it lasts, but about how likely you are to have a problem that interupts your trip. Diesels have no ignition system (a plus) but they are less tolerant of fuel variances (a negative). Modern ignition systems cause far fewer problems than ignition systems did 10 or 20 or more years ago. Overall, with modern direct injection fuel systems on gasoline vehicles, and other equalizing factors like turbos being installed on both versions, I don't think there is any significant difference in reliability.

You also mention maintenance costs. I wouldn't expect any significant difference. Both have fuel filters, air filters, and injectors that may require maintenance. Spark plugs are a non-issue these days. A bigger issue may be the skill level/familiarity of the technicians working on the newest generation of diesels in the first few years until they become more mainstream.

__________________
2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue