If he were elected president, former Massachusetts Gov. Mitt Romney says, he would cut companies' tax bills. But former House Speaker Newt Gingrich would cut them more than twice as much.

Romney would eliminate some people's capital gains taxes. But Gingrich would eliminate everybody's.

Romney would build more Navy ships to project American influence into the Middle East. Gingrich would build a moon colony, projecting it into outer space.

In dozens of campaign promises, the two GOP front-runners have provided a kind of aspirational self-portrait. These are the ideas that got them in the race and that would guide them in the day-to-day work of governing.

Romney's big ideas, while sometimes at odds with those of past GOP nominees, are largely within tinkering distance of the status quo. They mirror the man who came up with them: wonky and technical, but generally tailored for real-world application.

Gingrich's proposals go much further, requiring massive overhauls of the tax code, Social Security and the judicial branch - all at the same time. They are something like the candidate: epic, crowd-pleasing and ultimately a long shot.

Last week, Gingrich told a Florida audience that he would establish a lunar colony by the end of his second term in office. Some scientists say that might be possible; it would require mining ice at the moon's poles and using it to make drinking water, oxygen and hydrogen-based rocket fuel.

"You could have a sustainable moon colony with a dozen folks who were there and doing scientific research, engineering, planning, building roads," said Jack Burns, a University of Colorado professor.

Could this colony's population reach 13,000? Gingrich gave that number as the threshold for the moon to petition for statehood.

"Sorry, did you say 13,000? Wow," Burns said, laughing. "No. Certainly that's not going to be true by 2020."

In some areas, the two men agree.

Both want to repeal two key laws passed under President Barack Obama: the health care overhaul and the Dodd-Frank financial regulations. Both want to repeal the estate tax and get tougher with Iran. And both would amend the Constitution to ban same-sex marriage.

But in the differences between Romney and Gingrich, it is possible to see the gulf between the pragmatic and ideological wings of the Republican Party - and between two very unlike minds.

It starts with taxes.

"With Romney's plan, it's much more a plan that works within the confines of the existing tax systems," said Curtis Dubay, a tax specialist at the Heritage Foundation. "Gingrich's, to work, would have to blow the whole thing up and start from scratch."

Romney's plan would lower a corporation's tax rate from 35 percent to 25 percent. For individual taxpayers making less than $200,000 per couple, he would end taxes on capital gains and interest. The cost? Probably about $180 billion less in government revenue per year, according to the nonpartisan Tax Policy Center.

Gingrich would do far more. He would cut the corporate rate to 12.5 percent. He would eliminate all taxes on capital gains and interest. And he would allow individuals to opt out of the current tax code, giving them the option of a 15 percent "flat tax" with limited deductions.

The price tag? The Tax Policy Center estimated it at $850 billion a year.

Tinkering or re-creating

On Social Security, the two men exhibit a similar pattern. Romney would raise the age at which future retirees could collect benefits, adding "a year or two," he said in a debate. And he would tinker with formulas so that wealthier retirees would see their benefits grow less over time.

Gingrich, by contrast, wants to create a new kind of Social Security. He would keep the old system but allow people to opt into a separate system, in which they could keep their money in private, personal accounts. The same private-account plan has worked in Chile, Gingrich is fond of saying.

But it was installed while Chile was run by a military dictator.

"You don't have problems with Congress" in that situation, said the Heritage Foundation's David John. A President Gingrich probably would.

On immigration, Romney and Gingrich have called for a stepped-up crackdown on employers, who would have to use a system of identification cards to check that every worker is here legally.

Romney predicts that those who couldn't work would simply "self-deport." Gingrich has a more complicated vision. He has advocated letting some longtime illegal residents remain in the country - and letting new citizen councils choose which ones.

"It would never pass the Congress. And . . . if it ever passed Congress, it would be litigated for decades," because of the chance that immigrants could get unequal treatment in different towns, said Frank Sharry of the liberal group America's Voice.

"As a plan, it makes no sense," Sharry said. "As a political move, it's gutsy."

Marginalist or revolutionary

Romney's most grandiose plan might be his call to increase the construction of naval ships, from nine to about 15 every year. Gingrich has spoken about the need to "recapitalize our military infrastructure," without many details.

"The difference is, Romney is a marginalist, and Gingrich is more revolutionary," said Roberton Williams, a senior fellow at the Tax Policy Center. He said that Romney's approach, though less ambitious, seems more likely to win approval. "The problem with the Gingrich approach is that he would go in and throw the bomb, and then maybe there would be pieces that you would pick up afterwards."