The cheap one is a Frigidaire. Not sure of the exact model since I'm not currently near it, but I'm pretty certain it's equivalent to their FDPC4221AS model, if not that exact model. The price was under $400.
The expensive one that broke twice within 90 days was a KitchenAid that cost a bit less than $2000. I don't recall the model number. It had a stainless steel tub, three racks, interior LED lighting, fans to blow heated air to dry dishes, and all sorts of other fancy features, that, in hindsight, don't help clean dishes in the slightest.
The first break: half way through a wash cycle I smelled burning plastic in the kitchen. It seemed like it was strongest near the dishwasher, so I opened it up. As I did, the sound of the water and pumps stopped, allowing me to hear the sound of what would ultimately be the source of the smell: the fan that was meant to blow heated air during the drying cycle was grinding away at full speed and rubbing against its housing causing it to melt. I could only guess as to why it malfunctioned that way - it shouldn't have even been running until all of the wash cycles had completed. It got replaced a few days later with the same model.
The second break: I loaded it up, started the machine, and went to bed. When I woke up in the morning my entire kitchen was flooded with dirty dish water. This time, the plastic housing for the main pump had literally split in half. Not only did that allow water to just flow right onto my floor, but caused it to continue flooding my floor as it tried to fill the tub to the correct level. Since most of it was going on the floor, the float switch that signals when the tub is full never cut off the pump. Eventually I think the control board decided that was a problem and stopped the pump.
In hindsight, there was really no justification for buying the fancy one in the first place. Aside from all "amazing" features, the design and parts used to accomplish the actual cleaning are almost identical in every way. I felt like a real idiot for falling for the marketing.
Never again.
To be fair, I've little experience with Miele or Bosch dishwashers. I lived in England for about a year over 15 years ago and had a Miele there. I had to be diligent about keeping it clean, otherwise I'd end up with dishes that were even more disgusting than when I put them in, as it would very effectively deposit the contents of an uncleaned filter onto every surface before baking it to an enamel-like finish. Given how much people seem to love their Miele dishwashers I suspect my experience with them wasn't typical.