Amtrak is improving its wifi, it claims. Fine. The problem is, it’ll never be faster than your phone’s 4G connection.
Why? Because Amtrak’s wifi uses the same 4G network. So take your 4G, send the bits through an additional router, contend with your neighbors’ bits, and you’ve got Amtrak wifi. (This is true of the wifi on the bus too, it’s not about Amtrak specifically.)
Now, in theory, there are some decent reasons to use their wifi. If you’ve got a cap on your data plan, you can offload some of it to Amtrak. The train should have a big-ass antenna which might get a better signal that your device. Whether these things overcome the other issues, YMMV.
Wifi is really designed for small, controlled spaces, like apartments and offices. The telecoms’ stock in trade is data over large, uncontrolled areas. If you’re on the train, just use your phone.