Well, the first thing you need to understand is that it is not the case that we never picked up on railroads. America used to have the most advanced railroad network in the world, and when it comes to freight rail, we still do. What we have lost most of is passenger rail capacity, and the reasons this happened are varied, but generally boil down to "We made a conscious decision not to invest in the future of passenger rail transportation".

To understand why this is, it is important to know how early American railroads were paid for. It was a mix of government contracts, and free real estate. Passenger rail generally isn't profitable, even in Europe and Asia, and the two biggest examples of passenger rail systems that are profitable, the Paris to Lyon TGV and the Japanese Shinkansen, are higher priced express services that invest heavily in real estate ventures in their stations, and make more money from real estate than passenger services. This was also the case back in the early days of American rail, back before the "frontier" was closed, when the federal government was handing out free land like candy if people were willing to use it. If you built a rail line, you would get a lot of free land for doing so, and there are multiple ways to spin that land into a healthy profit. When I say government contracts, I mostly mean mail contracts. Passenger trains generally had a mail car because the Postal Service was paying the railroads to move the mail, and that money did a lot to subsidize passenger rail and make it profitable. There were also some cases, such as the Transcontinental Railroad, where the government really wanted a specific line built, and directly paid a railroad per mile for doing so, though this was not most rail lines.

The important take away here is, passenger rail in and of itself isn't really a money maker, and government investment, both in terms of giving out land and paying the railroads to do things, was critically important to making passenger rail actually work. And because of this, in 1873 a massive bubble in railroad investment burst, because a ton of people saw railroads as the up and coming technology and invested, especially with the government land grants sweetening the deal, and a ton of people built as much rail as they could thinking they'd rake in the profits, only to find rail operations weren't so profitable and there were too many players, and a lot of mergers and market consolidation ended up happening as railroads failed.

So, passenger rail wasn't hugely profitable, and was dependent on government support, even before the automobile arose as competition. And when the automobile does enter the scene, well, the government is absolutely entranced, and moves to support this up and coming technology. In the 1920s and 1930s, we already see the beginnings of car centric urban planning and people thinking of the car as the future of transportation, but the Great Depression really slows down the adoption of the car, though municipal governments are already enacting zoning policies that heavily favor the car. One cannot ignore the importance of race in this conversation either, though, because these car centric zoning policies weren't just implemented because people wanted cars and not public transit. People wanted to "clean up the cities" and "live in healthier environments", and these are really code terms for "get white people away from racial minorities and into their own nice, safe neighborhoods". The end effect is to cripple public transportation, but the intent is racial segregation, even (often especially) in jurisdictions outside of the Jim Crow South.

So we have railroads that are dependent on government investment, and a government more interested in investing in the automobile. In takes time for the government to fully realize that desire, as World War 2 prevents further adoption of the automobile, but World War 2 isn't great for passenger rail, either. During the war, the government asks people to ride intercity trains as little as possible to conserve fuel, and forces railroads to build more steam engines instead of diesel (diesel was needed oversees), engines that rapidly became obsolete post war outside of mountainous areas (steam engines could be better at hauling in steep grades compared to early diesel).

In the 1920s and 1930s, we see the rise of the streamlined locomotive in the United States, with streamlined steam in the 1920s and diesel in the 1930s. This sees struggling railroads trying to gain passenger share with high speed, aerodynamic trains, beautiful styling, and celebrity-studded services. And it both works and doesn't work. This is considered the golden age of American railroading, so it works in that people do indeed love these trains and want to ride them, but it doesn't work in the vein that the railroads still weren't turning a profit, and now weren't really getting government support. And these trains aren't really competing with the automobile. This is before the interstate highway system existed, so driving long distance from, say, New York to Chicago isn't as simple as just taking the freeway, and domestic commercial aviation is a very small industry at this time, so if you own a car and want to go from Chicago to Los Angeles, taking a train makes a lot of sense compared to driving or flying. As soon as the interstate highway system comes into being, we rapidly see passenger rail collapse, because suddenly driving makes sense. Especially since the federal government was providing car loans to veterans post-war, and local governments were forcing sprawled out housing developments and mandating large parking facilities that take up valuable real estate and give it to cars. One can point to the government implementing speed limits for railroads that prevent them from being faster than driving as a crucial factor, but this speed limit was implemented specifically because cash strapped railroads couldn't maintain their rails and the rails weren't safe for higher speeds, and railroads would have had to limit speeds or kill passengers, anyway. Some railroads could afford the technology needed to run above this speed limit legally, but that didn't address the underlying problems. Not to mention there were high taxes on railroads post-war, taxes which went to the interstate highway and car loans, which basically meant railroads were being forced to directly subsidize their main competitor.

So by the late 60s, passenger rail is in complete crisis, so the government forms a national railroad, Amtrak. I'm going to skip over a lot, here, but the important thing to understand is, joining Amtrak is a voluntary decision, and how it works is, a railroad has to give up all passenger services to Amtrak (you can't pick and choose). Any railroad at this time runs both passenger and freight, so Amtrak is getting the passenger services and rolling stock, but not the tracks or right of way. So suddenly passenger rail is operating on the same tracks as freight, but the tracks are owned by the freight railroad and the passenger trains run by an organization that isn't the freight railroad. Naturally the freight railroad is going to prioritize their own services, and force Amtrak to get out of the way of freight trains. Meaning Amtrak is wracked with delays and can't run on time, outside of the corridors like the Northeast Corridor where Amtrak does own the tracks. This is also why Amtrak doesn't have high speed rail outside the Northeast Corridor, and isn't allowed to electrify. The freight railroads own most track, and make the rules. And as said above, America has the best freight rail system in the world today.

And, well, there you have the biggest factors. Why is Europe better? European governments are willing to subsidize rail. Same with China. It is really hard to get numbers out of China, because they don't like to disclose this kind of financial information, but it is impossible that China isn't massively subsidizing high speed rail. Given that most Chinese airspace is closed to civilian aviation, creating huge traffic jams in what airspace isn't military only, it makes sense that China would want as many people on trains as possible.

As for sources, I will post them, but I need a few hours. I need to go to the store before they close, and I'll get to that after.