They question whether the sophisticated missile intercept system is technologically feasible and worry that building it could scuttle the 1972 Anti-Ballistic Missile treaty with Russia. The treaty requires an amendment before such a system could be built, but the Russians have refused to negotiate changes.
Both Bush and McCain say the system should be built as soon as possible and advocate scrapping the treaty if the Russians refuse to modify it.
Besides missile defense, the Democrats and Republicans are also far apart on another, divisive military issue: homosexuals serving in the armed forces. Gore and Bradley say gays should be allowed to serve openly, while Bush and McCain favor continuation of the Clinton administration's 1993 "don't ask, don't tell" policy.
That policy allows homosexuals to serve as long as they don't reveal their sexual orientation or act on it. Recruiters are barred from asking potential recruits about their sexual orientation.
Reshaping the military
The Republican candidates are driving the debate on reshaping the military from a heavily armored Cold War behemoth into a lighter, stealthier and more mobile force that can quickly respond to everything from skirmishes to full-scale war.
Both Republicans want to scale back or eliminate spending on Cold War-era weapons to free up money that can be used for new, high-tech weaponry. Bush points to the M-1 Abrams tank as ripe for cutting. McCain says the Seawolf submarine and B-2 bomber are "unneeded."
"Our forces in the next century must be agile, lethal, readily deployable," Bush said in a speech at the Citadel, South Carolina's military college. He vowed to resurrect ideas rejected by the Pentagon, such as the proposed "arsenal ship," a radar-eluding vessel packing long-range missiles and manned by a small crew.
And the Texas governor pledged that during the first five years of his presidency he would devote $20 billion to military research and development, an area that defense analysts say has long been underfunded.
Bush aides say the research money would come from the Pentagon's budget for new weapons purchases. That could put a crimp in programs such as the F-22, which is being built in Bush's home state.
While Bush favors construction of six F-22s, he'll decide after the election which programs to continue and which to cut, said Condoleezza Rice, a former Stanford University provost and Bush's chief foreign policy adviser.
Although all four candidates served in uniform during the Vietnam War, McCain is the sole combat veteran. He flew Navy attack aircraft, served 5 1/2 years as a prisoner of war and ended his military career as a Navy captain. He is a senior member of the Senate Armed Services Committee.
The Arizona Republican, a fierce critic of lawmakers adding projects to defense spending measures not requested by the Pentagon, said he could find $20 billion in savings in the defense budget by eliminating pork-barrel projects and making other savings, such as closing obsolete military bases.
"Our defense budget must be driven by our security needs, not vice versa," McCain said. "We must spend whatever it takes -- not one penny more, not one penny less."
Where the candidates stand
All candidates favor pay raises and increased benefits for military personnel.
BUSH: Favors increases in the defense budget to pay for new weaponry and research and develpment.
McCAIN: Favors increases in the Pentagon budget to rebuild the military and pay for new weapons systems.
GORE: Favors increases in defense and notes that the Clinton administration has proposed a $112 billion increase over the next five years, "the first long-term sustained increase in defense spending in a decade."
BRADLEY: Against increases in the defense budget and says further cuts can be made.
National missile defense
Build a national missile defense system that would protect all 50 states from a missile attack from a rogue state, such as North Korea. The initial system, as currently conceived, would include 100 interceptor missiles based in Alaska.
GORE: Undecided. Gore says such a program must be technologically feasible, cost-effective and able to comply with the 1972 Anti-Ballistic Missile treaty with Russia.
BRADLEY: Undecided. Bradley says he would "proceed cautiously," concerned that there is no proven technology. He wants to negotiate changes in the Anti-Ballistic Missile treaty with the Russians.
Gays in the military
The law prohibits homosexuals from serving in the U.S. military, though a 1993 Clinton administration policy, known as "Don't ask, don't tell," allows gays to serve as long as they don't declare their sexual orientation or act on it. Recruiters are prohibited from asking prospective recruits about their sexual orientation.
BUSH: Favors continuing "Don't ask, don't tell."
McCAIN: Favors continuing "Don't ask, don't tell."
GORE: Favors allowing gays to serve openly in the military.
BRADLEY: Favors allowing gays to serve openly in the military.