President Carter's final defense budget is so big it suggests that he was playing an old showbiz game with Rongal Reagan: Can You Top This?

The Pentagon under the Carter budget could commit itself to pay out a record $196.4 billion and spend $184.4 billion of it in the fiscal year beginning Oct. 1. That would amount to a whopping 14.5 percent spending increase over the current fiscal year.

Carter acknowledged that "the largest discretionary increase" in his budget is for defense. How Reagan will go him one better without bringing on the "economic Dunkirk" he is pledged to avoid is the question of the hour.

By favoring combat readiness over new hardware, the outgoing president invites Congress, if not Reagan himself, to add billions to the Pentagon's procurement accounts. This, of course, would increase the government spending Reagan is trying to curb.

When Congress asks for their personal opinions in coming months, military leaders are prepared to state that even the record peacetime amounts in Carter's farewell budget do not provide enough money to catch up with the Soviets any time soon.

Army leaders control that their modernization program is threatened by the way the dollar is divided, with an unusually large slice earmarked for such unglamorous accounts as spare parts to improve combat readiness; the Navy feels the shipbuilding program is too modest; the Air Force seeks that ever-elusive new bomber, and the Marines want more "lift" ships than the budget provides for taking their gear to distant trouble spots.

Reagan will most likely at least bow toward those military ambitions as he reviews the Carter defense budget. But any major changes would cost so much and take so long to fashion that the new president may opt to wait until next year to do more than tinker. But do not expect Congress to heed any pleas for restraint on defense spending.

The final Carter defense budget shows these policy trends:

Readiness -- Top priority given to former Cinderella accounts as extra billions are earmarked for longer training for soldiers, more steaming for sailors and larger stocks of spare parts to keep forces in fighting condition.

Persian Gulf -- Continued buildup of highly mobile forces for this hot spot, with, for example, $375.1 million to start developing long-distance CX transport for tanks and other heavy gear.

Strategic weapons -- Pursuit of a land missile so hard to hit that Soviets would give up on trying, thus closing the "window of vulnerability" opened up when Soviet warheads became accurate enough to destroy Minuteman missiles now standing in silos. The new missile, the MX, is slated to get $2.9 billion in fiscal 1982. A new submarine missile, Trident II, accurate enough to destroy Soviet middiles in their silos, also is generously funded, with $243 million earmarked for it in fiscal 1982, compared with $97.6 million this year.

Shipbuilding -- Deliberate rather than rush efforts to modernize the fleet. Navy leaders are protesting that the 80 new ships to be built under Carter's latest five-year blueprint is 17 fewer than the five-year total promised this time last year. The president's recommended rate of 16 a year is six ships below the number needed to bring the Navy up to the 600 ships Reagan has set as his goal. Congress will almost certainly add billions to this account, as it has in earlier years. This practice once prompted Sen. John Stennis (D-Miss.) to complain that he had to choose between "a Navy Navy, a Rickover navy and a congressional navy."

New bomber -- Carter is leaving this choice to Reagan, who assailed the president for canceling the B1. "Stealth" and a modified B1 are candidates for the Reagan bomber. Defense Secretary Harold Brown said yesterday that the amount earmarked for Stealth research to make planes virtually invisible to enemy radar is "very substantial" but secret.

Military pay -- Another 9.1 percent raise on top of the 11.7 percent approved for fiscal 1981 is recommended as Carter, reversing earlier stands, moves to make military pay comparable to wages of civilians doing similar jobs.

NATO cruise missile -- Pressing ahead with a ground-launched version to counter the Soviet SS20 missile targeted on Europe. Money for this missile would jump from $188.4 million this year to $485.6 million in fiscal 1982.

Marine AV8B Harrier -- Carter administration finally yields to Marine and congressional pressure and generously funds continued development, but not procurement, of this British-designed jet jump for supporting troops.

Aircraft buy -- The new emphasis on readiness cut here. Navy wanted money for 217 new planes; Carter trimmed the request to 121. Navy leaders complain it must buy 220 planes a year just to keep up with losses, setting the stage for a hot argument when Congress looks at how much of what is being bought with all these billions.

Brown, in discussing the budget at a Pentagon news conference yesterday, said the recommended increases "reaffirm the president's commitment to steady and sustained real growth in defense programs." He added that while there appears to be a national consensus today on the need to spend more on defense, "I have some concern" that this consensus may be "more fragile than some people think."

The Pentagon considers total obligational authority the most relevant figure in discussing growth of its budget. This total is money that can be obligated in a given year, though not necessarily spent until years later.

Counting the $6.3 billion in supplemental funds the Pentagon is requesting from Congress this year to cover pay raises and other extra costs, Brown said the fiscal 1981 total will rise to $171.2 billion. Carter is asking for $196.4 billion for this same account for fiscal 1982, representing an after-expected-inflation increase of 5.3 percent, Brown said. This would be on top of the 7.8 percent after-inflation increase between fiscal 1980 and 1981. The administration assumes a 9.45 percent inflation rate between fiscal 1981 and 1982.

As for spending, not counting the money other agencies will spend for such Pentagon items as nuclear warheads, Brown noted that the likely total will rise form $157.6 billion in fiscal 1981 to $180 billion in 1982. Under administration inflation assumptions, Brown said this would represent a 4.4 percent real increase.

Within the defense budget, the operation and maintenance account -- the one for spare parts, ship repairs and military exercises associated with getting in fighting condition -- jumped up 3.8 percent over fiscal 1981, after allowing for inflation. This was the biggest single increase. Research and development was second biggest among real increases, 2.5 percent, while the politically popular hardware buying account, procurement, ranked a poor fourth, going up only 0.6 percent.

Carter's defense blueprint for the next five years, fiscal 1982 through 1986, adds up to $1.17 trillion in spending and $1.27 trillion in total obligational authority. Conservatives are primed to argue that this is not enough.