DEERING, N.H. -- ''Both of us got sick of their bickering,'' Tim Seeger, 31, a real-estate appraiser, told me when I knocked one cold, starry night on the door of the home he and his wife, Carle, occupy in the woods near here.

Seeger was referring to the exchange of personal criticisms between George Bush and Robert Dole that marked the finale of the Iowa caucus campaigning. ''We don't care that much about their tax returns,'' he said. ''We want to know their game plan for the future.''

As the moment of decision neared for New Hampshire Republicans, the Seegers -- like many others interviewed -- were wrestling with the choice between the vice president and the Senate Republican leader.

Carle Seeger met Bush last week as he toured the General Telephone and Electronics offices where she works, but she is tentatively for Dole. Tim Seeger is leaning toward Bush, but wants to have more discussion with his wife after the final debate and television interviews.

When I asked these two informed and conscientious voters what they thought the difference would be between a Bush administration and one headed by Dole, they glanced at each other, then paused. ''I don't know,'' he said. ''Me either,'' she echoed.

It is not a question being asked very much as Bush seeks to keep his candidacy alive after the Iowa loss to Dole. But it is an important question, and one on which insights are available from the many people in Washington -- current and former members of Congress and of the last three Republican administrations -- who have served with Bush and Dole during the past two decades.

The comments I have collected from some of them in interviews over the past year are too diverse for easy summary. But a couple of points many of them make show how useful it may be (if this nomination battle is not quickly settled) to explore the question.

Going back through my notebooks, I realized that several of the officials had argued, in their own language, that the standard picture of Bush as the product of an extraordinarily long and broad executive apprenticeship, and of Dole as a consummate legislator, may be very misleading.

''If you think of an executive as someone who instinctively reaches out for answers to problems, that describes Dole more than Bush,'' said one man who knows them well. ''If you think of a good legislator as someone sensitively attuned to colleagues' views and ready to compromise, that fits Bush more than it does Dole.''

Another recalled Dole's announcing, in his first month as Senate Republican leader in 1985, that he would produce a Senate budget before the Reagan administration even submitted its own. The effort failed, but the former administration official said: ''I knew at that instant that Dole really wanted to be president, not just Senate leader.''

The picture that emerges from several of the interviews is of Dole as an aggressive, take-charge guy, strongly reliant on his own instincts. Bush, on the other hand, is more relaxed and reactive, ''a much better listener than he is a talker,'' said one former House colleague.

Those who think a president has to energize the White House and the government in order to lead the country may find Dole their man. Those who think it's more prudent to have a president who sits back, listens to all sides, withholds judgment and lets many problems solve themselves may find Bush's temperament preferable in the White House.

The former House member made a point that a number of others endorsed -- that Bush, who served in the House for only four years about two decades ago, may have more real friends on Capitol Hill than Dole does after all his years in the House and Senate. Bush has cultivated friendships there as vice president, partly by regular visits to the House gym, a great meeting place. Many describe him as a more gregarious person than Dole, whose working relationships are, they say, exactly that.

Another point that came up often in these interviews is the belief that a Bush White House and Cabinet would, predictably, be filled with familiar Republican figures of considerable talent, while the makeup of a Dole administration would be far harder to guess or to gauge. ''Dole has never relied much on other people working for him,'' another senator told me, ''while Bush has always relied on them and seen that they were good. Jim Baker {Treasury Secretary James A. Baker III} was his guy, and Baker is the best thing the Reagan administration has had going for it. Who ever came off the Dole staff that you remember as being anything special?''

These contrasts are suggestive, not conclusive. But they do indicate that if the Republicans decide to take their time in making their choice of a nominee, there are differences between Bush and Dole worth exploring. They are clearly not ideological opposites; indeed, they have had trouble finding issues on which they disagree.

But they are very different men, and their administrations could be of very different character.