In Philadelphia, all eyes are on the Democratic mayoral primary contest

W. Wilson Goode: managing director of Philadelphia under Mayor William Green. Mild-mannered. Not a taint of political scandal during his 17 years in public service, which includes a term as chairman of the Pennsylvania Public Utilities Commission.

Frank L. Rizzo: controversial two-term former mayor and one-time police chief , dubbed the ''toughest cop'' in the city. But the characteristic invective, the caustic wit are gone. Aides say he's ''the new Rizzo,'' who - if elected - will govern in ''a new spirit of partnership.''

This is the choice facing Philadelphia Democrats as the May 17 mayoral primary approaches. The outcome is likely to determine who wins the general election: Registered Democrats outnumber Republicans by nearly 4 to 1; and no Republican has been elected mayor of Philadelphia since 1950.

As in Chicago, the contest pits a black candidate, Mr. Goode, against a white one, Mr. Rizzo. So far, race has been nearly as subdued an issue here as it was during Chicago's primary campaign earlier this year.

One key issue is the city's economy. In a recent budget message, Mayor Green said that ''we are $99 million short of balancing a $1.4 billion budget and that deficit could be higher if we are not successful in getting state aid and if the economy continues to decline.''

Much of this city's widely touted downtown office and hotel building boom began during Rizzo's tenure in the early 1970s.

But Goode aides say at least part of the city's current economic difficulties can be laid at the former mayor's doorstep: The aides point to lucrative contracts municipal unions won during Rizzo's first term. But it's harder for Goode supporters to blame Rizzo for the city's loss of 39,000 jobs during the past three years of the Green administration.

Green himself contends he is not seeking reelection because he wants to spend more time with his family. Green's initial popularity has been severely tested by Philadelphia's mounting fiscal problems.

Rizzo's personality and past political style also are issues in this campaign. The Philadelphia Inquirer recently carried a cartoon likening Rizzo to a volcano spewing streams of lava all over the city.

To be sure, the former mayor has had a colorful political career. In 1976, more than 200,000 Philadelphians signed petitions to recall him. Only 145,448 signatures were necessary under the city charter, but the petition drive lost because Rizzo-controlled city commissioners determined that too many of the signatures were invalid. This sparked charges of corruption, which were never proved. The city's long-entrenched patronage system reached a zenith under Rizzo , as did the city's racial tensions.

But when Rizzo announced his candidacy in January, many Philadelphians noticed that to all appearances he had changed.

''I am ready to rededicate my life to lead as well as to serve this city and all of its people,'' he said. ''I say all of its people . . . and I mean just that - the young, the old, rich, poor, black, white . . . no matter where they live, work, or try to pursue happiness.''

Some political observers drew parallels between Rizzo and Alabama Gov. George C. Wallace, who turned a similar political metamorphosis into another term as Alabama governor last November.

But Rizzo's change in tone doesn't appear to be helping him. A survey released April 10 shows Rizzo nearly 20 points behind Goode.

Goode ''has managed to appeal to moderate whites as well as blacks, which puts Rizzo into a box of mostly appealing only to conservative whites,'' says Dr. James Pierson, an assistant professor of political science at the University of Pennslyvania here.

A graduate of Morgan State University in Baltimore and the Wharton School of Finance and Commerce at the University of Pennsylvania, Goode classifies himself as a ''problem solver.''

Goode insists, ''My campaign is not a drive to elect a black mayor. I prefer working with the mainstream, bringing all citizens together in a business-like administration.

''Our city needs positive leadership in five areas - jobs, housing, education , transportation, and public safety. Philadelphia deserves to have good, honorable government.''

Some observers say Rizzo's camp is getting desperate, despite protests that its candidate enjoys being the underdog. It's this quiet desperation that raises concerns about the issue of race.

''Up until now race hasn't been a major issue,'' says William Epstein, Goode's press secretary. ''But it's there on the fringe, and it's there on the fringe with Rizzo's assistance.''

Recently Rizzo vehemently attacked the Rev. Jesse Jackson - who came to town on his own to campaign for Goode - and Chicago's Harold Washington, with what many voters here considered racist remarks. Following the incident, Rizzo, Goode , and the four Republican primary contenders, pledged to sign a Fair Election Campaign Practices Code, drawn up by the Fellowship Commission here. For his part, Goode has refrained from abrasive and abusive language about his opponent or his supporters all along.