Tadic, who beat Nikolic to become president in a run-off in 2004, has asked Serbs to swallow their pride and pursue membership of the bloc whatever happens in the breakaway province.
Nikolic, a former ally of Yugosolav leader Slobodan Milosevic, wants Serbia to turn towards Russia, Serbia's only big power ally on the issue of Kosovo
"Serbia has two roads: the one to Russia is wide open, the other one to the EU is thorny and full of obstacles," he says.
Tadic, who says the issues of Kosovo and the EU are not related, has accused Nikolic of wanting to turn Serbia back to the isolation of the Milosevic years, when the country was an international pariah.
Nikolic has also highlighted disillusionment with the pace of reform in Serbia, where almost one million people remain unemployed and average salaries hover around $660 a month.
|Tadic defeated Nikolic to become |
president in 2004 [AFP]
The ethnic Albanian leaders of Kosovo have said that they will set the date for their declaration of independence after Sunday's result.
If Nikolic wins, political sources say that the Kosovars will declare independence the following weekend.
If Tadic wins, they will wait for a few weeks in deference to the EU's wishes.
Kosovo has been run by the United Nations since Nato drove out Serb forces in 1999 to halt ethnic cleansing during a counter-insurgency war.
A Nikolic victory could end the fragile coalition of Tadic and Vojislav Kostunica, the prime minister.
Kostunica has made the defence of Serb sovereignty over Kosovo the keystone of his policy.
He has attacked the EU's plan to deploy an 1,800-strong mission to supervise the transition UN rule, as a prelude to recognising the new state.
This week he said that he could not support Tadic's re-election bid because his coalition ally had refused to commit himself to pledging that Serbia would scorn any deal with the EU if it went ahead and supported Kosovo's independence.
Neither the EU nor the United States has shown any sign of backing down over Kosovo's independence, despite warnings from Vladimir Putin, the Russian president, that he will never accept it.
Polls close at 8pm (1900 GMT). First projections of the outcome are expected an hour later at the earliest.
Monitoring groups say they will be very cautious about calling the result.