Barzani's Kurdistan Democratic Party (KDP) and the Patriotic Union of Kurdistan (PUK), headed by Jalal Talabani, the Iraqi president, are expected to sweep the parliamentary poll.
The two factions have dominated the region's politics for decades and have been in power since 1991 when the region became semi-autonomous.
But a number of independent candidates like Nusherwan Mustafa, a wealthy entrepreneur and former PUK deputy, are working to break the PUK-KDP monopoly.
"We think that Kurdish society, after a political stabilisation, now needs economic, social and cultural reforms," Mustafa, who is head of the Change List, said.
Call for reform
Groups such as Change are hoping to capitalise on disenchantment with the ruling elite.
Hoda Abdel Hamid, Al Jazeera's correspondent, reporting from Irbil, said: "Over the past two months that group [Change] has had a lot of success ... it's really concentrated more on domestic issues rather than only the national agenda of the Kurdish people."
Critics of the Kurdish regional government point to widespread official corruption, abuses by security forces, media intimidation and an atmosphere they say stifles dissent.
Fereydun Rafiq Hilmi, an independent Kurdish analyst who was a former deputy minister of transport and communications, told Al Jazeera: "In fact, if you say anything about Barzani or Talabani, or if you criticise their methods, you are likely to be threatened even if you are outside the country."
He accused the administration of misusing public funds.
"The funds that are arriving in Kurdistan are going straight out again into their own bank accounts," he said.
"The people are still without electricity and clean water. They are still without any medical services. Education is geared towards changing the minds of the people to worship the leaders."
But Zagros Siwaily, a member of the KDP, defended the administration's record.
"I wouldn't use the word corruption, I would use the word mismanagement," he told Al Jazeera.
"Due to the problems that we've had the administration has not managed to fully provide all of the services that the people need.
"Remember that in Kurdistan we've inherited a region in this part of Iraq that has gone under decades of under-investment and mismanagement by the previous regime," he said, referring to the rule of Saddam Hussein, the former Iraqi president, ousted in the US-led invasion of Iraq in 2003.
On a national level, in the run up to the elections, tensions have been high between Barzani's administration and the central government of Nuri al-Maliki, the Iraqi prime minister, over Kurdish claims to 16 disputed areas.
|Barzani, left, is expected to be re-elected
as regional president [AFP]
Those areas include oil-rich Kirkuk, and parts of three historically Kurdish-populated provinces - Diyala, Nineveh and Salaheddin.
During a visit to Washington on Thursday, al-Maliki noted that these tensions were among "the most dangerous issues that have been a concern for all the Iraqi government".
But he said he expected to resolve the standoff, saying: "I am confident that we will be able to resolve all these issues not only with the Kurdistan region but also with other provinces."
Barzani has insisted he will not "compromise" on the Kurd's longstanding claims to Kirkuk and wants the issue to be settled by a referendum - called for under the Iraqi constitution - despite opposition from Kirkuk's Arab and Turkmen residents.
The country's natural resources have increasingly become a point of disagreement with the central government and have hamstrung exploitation of much of Iraq's massive proven reserves.
On June 1, the Kurdish administration began exporting oil for the first time, but Baghdad is contesting the region's right to sign contracts without central government approval.
Final results in the election are not expected for several days as ballots must be collected in Irbil, the regional capital, before being flown to Baghdad to be counted.
Polls opened at 8am local time (05:00GMT) and are due to close at 6pm (15:00GMT).
Though Saturday sees the main vote, more than 100,000 Kurdish members of Iraq's armed forces cast their vote on Thursday, along with police, prisoners and the sick.