First of all, unfortunately, I don't have scientific papers or statistics about this (I found statistics on age, on mileage and on % diesels, but not age and mileage wrt. diesel or gasoline) - and googling isn't very effective because tons of non-scientific stuff comes up. But I hope I can contribute a few hints of evidence, and I want to point out a number of confounding factors which have a large influence on the lifetime of an engine.
And one important consideration is what "more freqently" means. Per 100.000 km? Per year (difficult for new cars)? Per engine (i.e. which percentage of engines "dies" by engine failure - in my experience: very few of both sorts)?
Summary: a search on car sales pages indicates that gasoline cars can reach a mileage of several 100.000 km nowadays, like diesel cars. Though (at least here in Germany) diesel cars are preferred by the long distance drivers. While such preference is probably not only based on expected lifetime, and that may have a lag from the long-lasting reputation of the diesel even if this is not true any longer, it also isn't evidence in favour of diesels being dramatically worse than gasoline engines.
I came across two more newspaper articles in German language with claims roughly along the cited one:
The first one
points out that the old "everlasting" diesel engines had low power both compared to gasoline engines and compared to modern (turbo) diesel engines.
This factor may be particularly important for German cars makes, because taxes are calculated here not from the engine power but from engine volume. This poses a constraint that works towards high power per volume, and high rpm, thus also towards higher mechanical demands. German Wiki agrees with me that this causes shorter lifetime of the engine
The 2nd newspaper article
claims that the gasoline engines got much better, and also mentions that the higher power of the diesel engines (with comparable volume) essentially costs lifetime.
A rumour I've heard which goes into this direction concerns diesel engines which are/were available both with and without turbo, the turbo version is said to be far more prone to engine failure. This was attributed to the higher power of the turbo version of otherwise equal engines.
Anecdata in this direction is that I've seen more "car to be sold with engine failure" ads of the VW Type II T3 turbo than the SD at ages of 15 - 20 years. But I don't know in which proportions they were sold (but when those were new, the SD was the "normal" one). And they are not what one would call a modern diesel today.
Kown factors for the longevity of car engines are
- the higher the specific power (power / engine volume) the shorter the engine life
- driving habits/profiles are very important as well
see e.g. German Wiki (the English one merely says "Drive with habits that don't take years off the car").
Diesel engines used to be not only lower specific power but also slower max speed and lower power / car weight.
This means that preferred driving style could pretty much decide the type of engine. Gasoline for "sportive" driving style (which is much more demanding on the car, lots of load-cycle changes), diesel for calm/slow driving style.
The "long-lasting" was an important sales argument, aiming at people who drive a lot. This means, that those cars were more likely to end up far more in long-distance driving than gasoline cars at the time. While the question is about modern diesel engines, I think this historic situation needs to be taken into account because that is where the long-lasting reputation of the diesel comes from. Note for judging the OP's article that it was also not a "cheaper" but a "more economic if you go long distances" reputation. And it was no "cheaper repair" reputation.
Meanwhile diesel car engines have much higher specific and total power. Look e.g. at the BMW N57 engines (e.g. 242 kW, 4.4 l) or the Mercedes-Benz W221 (235 kW, 4 l) Those BMW 7 series and Mercedes S class diesel cars are restricted to vmax 250 km/h, just like the gasoline ones (though these series have gasoline engines with still more power).
Hints about the lifetime of modern diesel engines.
- Searching at this used car sale platform for cars > 150.000 km (highest low limit I can set there), I get roughly
- 41000 diesel vs. 12000 gasoline cars for the 5 - 10 year old and
- 14000 diesel vs. 1000 gasoline cars for the less than 5 year old.
- for comparison, 48% of the new cars in Germany are currently diesels.
- for older cars , the percentage of diesel cars drops to about 10%.
But other things change as well. The higher price segment of the ca. 15 - 20 year old cars is dominated by Porsche (gasoline), with a few armoured Mercedes and other "specials". The low price segment is full of old gasoline cars.
In 1995, only 1/6th of the new cars were diesels. And it is more difficult to sell a Diesel car of this age, because of the tax laws. A comparable diesel to one of the low-price gasoline cars of that age easily costs 3x as much taxes as the gasoline - and hundreds € difference in taxes are taken into account for a market where 40% of the cars are sold for < 1000 €. This also shows the limits of trying to pick evidence this way: obviously, if diesel cars basically break down earlier than gasoline ones, the picture would be the same.
Conclusion of this search: long distance drivers certainly prefer diesel (the < 5 year olds). Nowadays, gasoline cars can reach the same mileage of several 100.000 km (inspecting the higher mileages of the < 5 and 5 - 10 year old cars - disregarding > 999.999 km, as one needs to carefully look for typos that add a digit and obviously meaningless mileages like the 999999).
However, there are other engine segments, where modern diesel engines last much longer. Have a look at trucks and omnibuses. The truck search at mobile.de the median of the < 5 year old trucks on sale made 600.000 km till now. These engines have much lower specific power, and long-distance driving profiles.
Side note: there is a trend to turbos for modern gasoline engines as well. So one more expensive part that can fail for gasoline cars as well.