The Senate last night approved an Amtrak financing bill that, similar to a House-passed version, cuts about 16 percent of the least-used miles from the nation's rail passenger system.

Although President Carter had wanted the system reduced by 43 percent, the compromise measure, passed last night, had the blessing of the administration which backed off its original demands as rail usage boomed with the coming of the energy shortage.

Proponents of retaining the entire 27,500-mile system for another year lost, as they did on a close vote in the House last week. The Senate freeze, offered by Sen. John Melcher (D-Mont.) was rejected 65 to 35.

The version that passed by a vote of 89 to 11 was proposed by Sen. Patrick J. Leahy (D-Vt.)

The differences in the House and Senate versions are largely of a technical nature, and are unlikely to hold up getting the bill to the president's desk in time for the system to be cut back by the start of the new fiscal year on October 1.

The decision on which trains will be eliminated will not be nailed down until October 1, so that Amtrak can use the latest rider figures to determine the routes that meet the criteria outlined in the congressional mandate.

But among the likely victims, according to Melcher, are five trains that have shown marked increases in passengers in recent months, and are now running at near capacity.

Trains that will be "executed" as a result of the cutback, Melcher said, are: the New York-to-Kansas City "national Limited;" Chicago-Miami "Floridian;" Chicago-Houston "Lone Star," Chicago-Seattle "North Coast Hiawatha," and one of the New York-Florida trains, the "Silver Meteor" or the "Champion."

Saved by the criteria -- a train must average 150 passengers per mile and lose no more than 7 cents a mile -- are the Montreal-to-Washington "Montrealer," New York-New Orleans "Southern Crescent," Chicago-Washington "Cardinal," and either the Silver Meteor or the Champion.

Two trains that don't meet the standard criteria probably will be saved by a "regional balance" amendment offered by Sen. Frank Church (D-Idaho). It says that no region of the country can be without a passenger train, thereby rescuing the Salt Lake City-Seattle "Pioneer" and a Texas train, either the Chicago-Laredo "Interamerican," or the "Lone Star."

Commuter trains now operated by Amtrak won an 18-month reprieve, through April 1981, to give state and local governments time to figure out how to finance their operation.

Sen. Russell B. Long (D-La.) chairman of the Commerce surface transportation subcommittee, led the fight against retaining all existing trains. Sen. Howard W. Cannon (D.Nev.), chairman of the Commerce Committee, warned that the freeze would result in a presidential veto. Long said Amtrak, which was losing $40 million in 1970, "when they sold us this turkey," is losing $600 million now "and heading for a billion." The subsidy amounts to $20 a person "for the 99 percent of Americans who never ride a train, "Long thundered.

Sen. John C. Danforth (R.Mo.) said he favored the 43 percent cutback originally sought by the Carter administration, but agreed to the compromise, even though some of the routes to be retained are "frills in the federal budget."

To Danforth, "the issue is money." The administration proposal would have cost $550 million for each of the two years the authorization covers; the Leahy compromise will cost $605 million a year, and freezing the entire system would have cost $720 million a year.