President Reagan's budget cuts are taking a far greater share of federal dollars away from ailing industrial cities with high unemployment and declining populations than from booming Sun Belt cities, according to a study released yesterday by the congressional Joint Economic Committee.

The study, which surveyed 48 cities, found this Catch 22: the higher the rate of unemployment, the greater both the decline in federal aid and the likelihood that a city has raised taxes and cut services in recent months to avoid budget deficits.

Part of the explanation seems to be that the Reagan program has cut most sharply into federal grants having distribution formulas favoring older industrial cities.

On the other hand, Sun Belt cities have frequently received more federal dollars this fiscal year from general revenue-sharing because its formulas rely heavily on population and they grew in the 1980 census.

Philadelphia--beset by unemployment, strikes and shrinking public services--lost more than half of its $100 million in federal jobs-training money and $6 million in general revenue-sharing because its population had declined. The city has struggled to keep some of the workers formerly paid out of federal jobs-training funds, adding to its financial pinch.

Booming Phoenix is receiving about the same number of federal dollars this fiscal year as last. Like Philadelphia, it lost jobs-training money, but that was compensated for by the increase in revenue sharing. Phoenix, however, did not pick up workers laid off because of cuts in the federal jobs program. Its citizens are using the added revenue-sharing dollars for police and fire protection and street maintenance.

This difference in budget-cut impact is likely to be an issue as Congress considers further spending reductions.

Rep. Henry S. Reuss (D-Wis.), chairman of the Joint Economic Committee, fired several salvos in the report.

He said cutbacks have left the old cities in "deepening distress" and he predicted that the long-range effect would be to "render these cities home for the most dependent segments of society--the undereducated, the unemployed, the aged and the minorities."

Reuss dismissed Reagan's claim that older cities will share in the general economic recovery that the president has said he hopes to bring about with his budget and tax cuts.

"A city which is in the process of raising taxes and cutting services and which is resting on a decaying infrastructure provides no inducement to business expansion," Reuss said.

According to the study, the older cities are cutting health programs most sharply as they struggle to maintain current police, fire and sanitation services.

Sun Belt cities have their problems, too, the report indicated.

They are growing faster than their services can expand and, as a result, are suffering with overcrowded housing and schools, and inadequate transportation systems. Many have deferred large construction projects over the last year, presumably because interest rates on borrowings remain so high.