No matter who wins, the vote seals a swing to the right after four years of social democrat rule and two five-year terms for leftist President Aleksander Kwasniewski who could not run again.
Voting began at 6am (0400 GMT) and exit polls are due after stations close at 8pm.
Nearly 30 million Poles are eligible to vote in the fourth presidential election since the collapse of communism.
The last opinion surveys showed voters virtually evenly split in an election that has turned into a plebiscite on whether Poland needs more free market mechanisms after 16 years of often painful reforms or should focus on shoring up the welfare state.
Poland's ex-communist left brought the country into the European Union last year, but its popularity faltered because of a series of scandals and failure to curb unemployment.
That led to a landslide win in last month's parliamentary election for their old foes from the pro-democracy Solidarity movement that toppled communism.
The vote signals the end of rule
for Aleksander Kwasniewski
A first round of voting narrowed the presidential field to Tusk and Kaczynski, both former Solidarity activists.
Their Law and Justice and Civic Platform parties won the general election and they are trying to form a coalition government.
"I always vote, though a third time in a month was a bit too much. The choice was poor, but I picked Tusk, because his views are closer to mine," said Krzysztof Luro, 25, in Warsaw, who cast his vote on his way to work at the post office.
The bitter rivalry between Tusk and Kaczynski has slowed coalition talks and analysts expect whoever wins on Sunday will be able to tip the balance of power in the coalition.
The president is commander in chief of the army, can propose or veto legislation, nominate prime ministers - who hold most executive power - and, in some cases, dissolve parliament.
Lech Kaczynski promises a break
from post-communist Poland
Soft-spoken Tusk, 48, has cast himself as a moderating force who can unite Poles, mend rocky relations with neighbours Russia and Germany and put the nation of 38 million in the EU mainstream.
Kaczynski, 56, promises a clear break from post-communist Poland, a war on crime and corruption under the banner of moral renewal and a return to basic family and Christian values.