The race for the Senate seat from California skipped across the battlefields of Europe Wednesday night in the first full-scale debate between Republican Pete Wilson and Democrat Edmund G. (Jerry) Brown Jr.

Wilson, mayor of San Diego, and Brown, governor of California, spent much of the hour televised from here to most major California cities arguing over how to block the Soviet threat to Western Europe, although they also disagreed on immigration policy and Cuba. Both spoke forcefully, but the debate ended in an apparent, and uncharacteristically polite, draw.

Wilson called for a firm American position to discourage Soviet adventures and praised the Reagan administration's efforts to begin nuclear arms reduction talks in Geneva. He sought to blunt Brown's attacks on him for failing to support the popular nuclear freeze movement by arguing that "the duty of America is not to freeze the terror. . . but to dismantle it."

Brown, as he has with previous conservative challengers, seemed to go out of his way to please Republican listeners. He quoted the late Dwight D. Eisenhower, spoke warmly of the anti-insurgency Green Berets, decried Soviet mischief and called for a massive buildup of U.S. and allied conventional forces in Europe.

The latest polls show the two running about even, with Wilson having dissipated a big early lead.

Last night's debate was a counterpoint to their new $300,000 television ad campaigns that attempt to assign the blame for the current recession and high unemployment.

Brown has dropped his controversial ad that accused Wilson of opposing a nuclear arms freeze and is shifting his attack to Reaganomics, which he blames for high interest and unemployment rates.

Wilson, in turn, is trying to make Brown the campaign issue. One ad blames California's taxes on Brown's profligate spending as governor; another blames the huge federal budget deficit and high interest rates on "overspending by congressmen and senators who have done to the federal budget what Jerry Brown has done to California."

In the debate, however, Brown chided Wilson for not supporting the freeze movement. The mayor's insistence on an immediate arms reduction was wrong, Brown said, because "when you're going down the road at 60 miles an hour as we are in the nuclear arms race, you can't put it in reverse and go the other way until you at least stop."

The two appeared to agree on several issues concerning the need to promote foreign trade and on support for Israel, but Wilson chided Brown for advocating recognition of Cuba while Fidel Castro attempted to export revolution to other South American countries. Brown replied that Republican Secretary of State Alexander M. Haig Jr. had begun the latest initiative toward Cuba and that it ought to be pursued with help from the Mexicans.