Virginia U.S. Senate candidates Andrew P. Miller and John W. Warner are racing into the home stretch of their contest in a cloud of rhetoric over personal integrity, negative campaigning and campaign financing.

But behind the taunts and verbal jabs lie profound differences between Democrat Miller and Republican Warner on major issues, especially federal taxes and the role of the federal government in education.

Warner favors a much deeper cut in federal taxes than does Miller, who has said it would be "irresponsible" and inflationary to approve a tax reduction that is not offset "dollar for dollar" by reduction in federal spending.

The Republican advocates his party's proposed reduction in individual taxes of 33 per cent over three years. He also favors a 6 percent reduction in corporate tax rates. He called the tax bill finally passed by the 95th Congress "a hoax" and a "knuckling under to the President." The bill will not provide a net tax reduction to 80 percent of the taxpayers after the effects of inflation and a social security tax increase next year.

Miller advocated a tax reduction to "offset the new higher social security taxes." He has not been as forward as Warner in attacking the tax measure approved by Congress but has said in answer to questions that it does not provide "meaningful relief" for most taxpayers.

Despite their fundamental difference over the size of a tax reduction, both take identical positions on other tax issues, positions that are generally acceptable to Virginia's fiscal conservatism.

Both favor a reduction in capital gains taxes, and have voiced no opposition to the one approved by Congress. Both favor "indexing" of tax tables, and adjustment that would prevent the automatic tax increases that result from income increases due to inflation.

Both also favor a constitutional amendment requiring a balanced federal budget, but Miller regularly accuses Warner of suggesting that a balanced budget cannot be achieved by 1981, as Miller believes. Warner insists that his commitment to a balanced budget is as strong as Miller's but he accuses President Carter and Miller of "holding out false hope" in the light of current deficit projections.

While the candidates say they believe taxes, inflation and government spending are the issues that preoccupy voters, they have had their sharpest policy conflicts over the federal role in education.

Miller helped nail down his endorsement by the Virginia Education Association, but risked running afoul of Virginian distrust of the federal bureacracy, by supporting the proposal to create a federal department of education.

Warner has called this "the Grand Canyon between us on issues." He has contended that the new department will "grow and grow and grow" and finally erode state and ocal control of schools.

Miller also has said he favors the National Education Association goal of one-third funding of schools by the federal government "provided that other important national priorities are neither compromised or delayed."

Warner strongly opposes the proposal on ground that it would undercut state and local responsibility for schools and would lead to new federal spending that he estimates at $40 billion a year. Of federal aid to education and other state programs, he repeatedly says, "Every dollar that comes down the pike from Washington is followed by a new regulation right behind it."

Miller insists that the only way to control waste and inefficiency in the Department of Health, Education and Welfare is to subdivide it into new agencies. He therefore advocates not only a new department of education, but new cabinet agencies for health and welfare.

Other issues on which the candidates differ sharply include: Equal Rights Amendment

Miller is for it, Warner against. But both opposed extension of time for ratification of the proposed amendment by the states, saying that casts a constitutional cloud over final state action. Food Stamps For Strikers

Warner opposes providing food stamps to strikers on grounds that it would be government interference in a labor dispute. Miller says the stamps should go to families of strikers but not to strikers themselves. His proposal would permit strikers to get the benefit of reduced food costs at home. Voting Rights Act

Virginia is one of 22 states where elections are subject to federal regulation because of past discrimination against minorities. Warner opposes renewal of the law when it expires in 1982 because he "knows of no instances of voter discrimination in Virginia." Miller agrees that voter discrimination has long since ceased, but would approved renewal of the law if it were applied to all 50 states. if not he say he would vote against it. D.C. Representation

Both oppose the proposed constitutional amendment to give the District of Columbia full representation in Congress on grounds that it would effectively turn the city into a state. Warner says he would support giving the city back to Maryland. Miller supports voting representation in the House of Representatives for the city. City Service Pensions

Miller advocates transfer of federal civil servants to the social security system provided that none of the benefits they have earned under their current retirement system are lost. Warner supports continuation of the present system for civil service employees but would put members of Congress in the social security retirement system. Campaign Financing

Warner oposes government funding of political campaigns. Miller opposes total financing by the government but says he would support a system of government grants to match individual contribution.