The charge and countercharge of his latest debate with Mayor Edward Koch was over, and, in his car, Lt. Gov. Mario Cuomo was supercharged.

"Did you hear what he said? Did you hear him on pensions? He made my case for me. He made it a bigger issue. He . . . ."

Campaign manager William Haddad quietly interrupted. "He was very good today, Mario. You were good, but he was good too."

" . . . I had him on that 12 percent. He didn't know what he was talking about . . . . Now, we have to concentrate on getting the people to know who I am."

"No," Haddad said. "They know who you are. They don't know what you are."

That is the difference between Cuomo and Koch.

Not long ago, the cognoscenti were pleading no contest on the Democratic nomination for governor of New York: Koch all the way, they said. But now it has become very much a contest--a genuine battle between an often conservative mayor who is known for his outspoken stands and outrageous outbursts, and a liberal lieutenant governor who is known for speaking eloquently on the issues but leaving no firm public impression of what he stands for.

If Koch defeats Cuomo in the Sept. 21 primary, as he is now a cautious favorite to do, he will still face considerable political problems caused in part by Cuomo.

Cuomo already has the Liberal Party nomination for governor, so he will be on the November ballot regardless, to siphon liberal Democratic votes from the unabashedly more conservative Democratic nominee.

All of this will work to the benefit of the Republican nominee, who appears likely to be multimillionaire Lewis Lehrman. He already has the Conservative Party nomination, is heavily favored to win the GOP primary and shares the Jewish origins and hard-line inclinations that Koch celebrates. He also is blessed with the personal resources to outspend all of his fall rivals combined.

That could mean New Yorkers will be treated to an autumn battle of two major party candidates trying to out tough talk each other.

"I'll make a deal with you," Cuomo said to Koch. "You don't do a commercial on the death penalty and I won't."

"We're not going to let you decide our commercials," Koch replied, and the debate in the offices of The New York Times rolled on.

Crime is a major issue among voters in both Democratic and Republican primaries, polls show. Koch favors the death penalty; Cuomo is opposed. It was that way in 1977, when Koch defeated Cuomo in a mayoral primary in which they debated 23 times.

During their recent debate, Cuomo complained that Koch is telling voters that the only difference between them is their positions on the death penalty. That prompted Koch to say that he has never said anything of the sort.

Koch, meanwhile, found fault with Cuomo's use of the phrase, "the politics of electrocution." And he went on to say that the use of the death penalty, after all, "is acceptable in the Bible."

So it goes. Early this year, the polls were saying that Koch was ahead by 30 or 35 points, but the Koch and Cuomo camps always figured it was much closer than that.

A Gannett newspapers poll in June gave Koch a narrow eight point lead, 46 to 38 percent. Cuomo's polling is not quite so optimistic, however, and Koch's shows his lead is somewhat larger.

Cuomo clearly bested Koch in their first debate last month, as he attacked and the mayor gave a lackluster defense of his record. In his inimitable style, Koch convened a news conference the next day to concede his defeat in the debate, and since then the debates have featured equal measures of thrust and parry.

The death penalty is shorthand for tough-on-crime/soft-on-crime. That infuriates Cuomo because his family has been subjected to the brutality of crime. His wife was mugged in the presence of his youngest son this year, and one of his daughters has been physically attacked twice.

Cuomo firmly makes the argument that the institution of capital punishment would not have prevented these assaults, and he lays out his war-on-crime program.

But he knows the political realities of his position. And the politician who likes to intellectualize every question, and respond in intricate paragraphs, is reduced to monosyllables as he ponders the impact.

Reporter: How does your position on the death penalty affect your campaign prospects?

Cuomo: It hurts me.

Reporter: In what regions?

Cuomo: Everywhere.

Reporter: What are you going to do about that?

Cuomo: Nothing.

"For me," the mayor said, "the key thing is to get a lot of people voting . . . . I always do my best when the vote is large."

This is because of the nature of the people who vote in New York's Democratic primaries, he said in an interview. The turnout is usually small, about 25 percent, which means a disproportionate number of the voters will be "single-issue voters . . . activists." He elaborated:

"Liberal. Militant. Arch."

These are not Koch's kind of people, and so he is pushing to broaden the turnout. He has already managed to broaden the interest in his candidacy, although not necessarily in the manner he would have most preferred.

It started with his comments in a Playboy magazine interview earlier this year in which he ridiculed the people who live in the upstate and suburban communities he is now courting.

"Have you ever lived in the suburbs?" he said in the interview. "I haven't, but I've talked to people who have, and it's sterile; it's wasting your life."

And: "Rural America? That is a joke . . . . Let's leave out rural America, with the cows . . . . where people wear a gingham dress or a Sears, Roebuck suit . . . ."

And: " . . . living in Albany . . . is small-town living at its worst."

It is not surprising that the polls show that Koch has his greatest trouble in Upstate New York. The Gannett poll showed Cuomo leading Koch by 12 points upstate, the only region that Cuomo controlled.

Surprisingly, Koch's region of greatest strength is in those "sterile, wasting-your-life" New York City suburbs of Long Island and Westchester and Rockland counties. The Gannett figures gave the suburbs to Koch by 60 to 30. Why?

"Because he says he'll stop crime," Cuomo said. "It is perceived that he'll be tough on the people they're afraid of." Koch's advisers add that the suburbanites apparently were not offended by the Playboy interview because they watch New York City's television stations and are used to the mayor's loquacious ways.

The greatest concern to the mayor and his advisers is that Koch is not doing as well as they would like in his own city. The Gannett poll gave him a 48-to-36 edge. Cuomo carries the black and Hispanic vote in the various polls, but the mayor had another explanation for the relatively narrow lead he has in his city.

"I believe it is because there are people in the city who say I've been such a good mayor that they do not want me to go," Koch said.

At times, the crime issue gets to Cuomo, and he explodes with an expletive he says he believes will drive his point home to the public once and for all.

"You know what they want? They want Tomas de Torquemada in a robe!"

He was asked if this reference to the Spanish Inquisitor General isn't a bit obscure. "De Torquemada?" he responded. "Everyone knows de Torquemada." Then he thought again.

"Well, maybe you guys had better translate it. Call him Tommy the Hatchet."