Amtrak and VIA Rail Canada are two similar, but at the same time different, animals. Both are government-run corporations (what we call in Canada a Crown Corporation), however, they differ in the way they were created.
Amtrak was created through actual legislation in Congress; to consolidate the freight railway's passenger service into one entity. Amtrak was given a mandate by Congress to provide passenger rail service in America (please correct me if I am wrong).
VIA was created by order-in-council (the Canadian equivalent of an executive order) by the Trudeau government in 1978. There is no "VIA Rail Canada Act" or anything similar (attempts to do so have been stymied because the legislation "dies on the order paper"- i.e. Parliament gets shut down either b/c of an election or other means before the bill got passed). VIA had been in existence shortly before it became a crown corporation- CN created VIA as a marketing scheme for its passenger rail service and CP later added its passenger service around the time VIA became a full-fledged crown corporation.
Both are political footballs, subject to the whims of the government of the day. Amtrak has been more fortunate than VIA in that many congressmen and women have pushed for funding for the preservation of service in some circumstances. Canadian governments have been more brutal with VIA in terms of budget cuts. in the 1980's and 1990's, VIA lost half of its transcontinental services (The Super Continental and The Atlantic were cut- Imagine the Empire Builder, Lake Shore Limited, California Zephyr, Sunset Limited, Texas Eagle and Cardinal cut to get the idea of the magnitude). The Canadian was switched to the Northern CN line (the old Super Continental route) in order to serve "more remote communities" (but in reality to secure political support in ridings/districts along the route). Service to Cape Breton Island in Nova Scotia and other Atlantic Canada services were cut as well.
Via's rail network today consists of:
The Quebec-Windsor corridor
The Canadian (Vancouver-Toronto over the northern CN line)
The Ocean (Montreal-Halifax via Quebec)
The Chaleur (Montreal-Gaspe)
The Malahat (on Vancouver Island)
The Skeena (Prince Rupert-Prince George-Jasper)
The Hudson Bay (Winnipeg-Churchill)
The Lake Superior (Sudbury-White River)
The Abitibi (Montreal-Senneterre)
The Saguenay (Montreal-Jonquiere)
Services on Amtrak and VIA also differs depending upon class and train.
Amtrak Coach class and VIA's Comfort class are similar in terms of price and service. However, many VIA trains don't have a "lounge" car per se and have cart/take-out service for food and beverages.
VIA 1 in the Corridor is the equivalent of Business/First class offered on Amtrak, but more akin to Acela First Class. Meals are included in your fare and wi-fi is offered on select trains.
VIA also offers Totem Deluxe Class on the Skeena during the peak season. Totem Deluxe gets seated in the Panorama glass dome car and also gets exclusive access to the Park car (Observation Car/dome). Meals are included in the fare. It is a tourist package, both in service and in price. (If you want a really cheap dome experience through the Rockies, take the Skeena off-season. Comfort class has the Park car then and you can get round-trip Prince George-Jasper for about $100 USD at the lowest price per person incl. taxes
).
Sleepers class depends on the train. The Canadian has the famous Silver & Blue class, which during the peak season can cost as much as
$5000 CDN ONE WAY Vancouver-Toronto. But Silver & Blue is pretty much like taking a land cruise- miles above and beyond anything Amtrak offers (yes, even the relaunched Coast Starlight). The Ocean offers Easterly class which is similar to Silver & Blue.
There is also "Comfort Sleeper" on the Ocean, Chaleur, and Hudson Bay. You get a sleeper, but meals are not included, and it is less expensive than the premium sleeper classes. Amtrak's sleeper service is relatively consistent by comparison in terms of price and service.