Half the people of Wales want the Welsh assembly to have the most influence on their lives of any government.
Huw Edwards says People's Voice can raise awareness of voting
Some 35% said the assembly government currently had the greatest impact on Wales, compared with 30% who said it was the UK government.
The poll for new BBC programme People's Voice also found health would be the most important single issue at the general election expected in May.
People's Voice with Huw Edwards is on BBC1 Wales at 2235GMT on Tuesday.
The ICM poll of 1,000 people asked about how Wales had changed since the assembly first sat in May 1999.
A total of 31% said things had improved, while 21% thought things were worse.
But 43% replied that the assembly had made no difference, while 4% said they did not know.
Q. What's the most important general election issue?
Law and order: 8%
Pensions/elderly care: 6%
Source: ICM poll of 1,003 adults interviewed 11-20 Feb
The poll also looked at who people thought had most effect on Wales, and 35% said the assembly government.
Of those asked, 30% thought it was the UK government, 16% their local council, and 10% the European Union.
But when asked who should have most influence in Wales, 50% replied the assembly government.
Under a quarter - or 23% - said Westminster, 20% wanted their council, and just 2% said the EU.
Q. What Welsh issue concerns you?
Law and order: 6%
Assembly/education (both 5%)
House prices/affordability: 4%
Unemployment/low wages: 4%
Council tax: 3%
With a general election widely expected in May, people were also questioned about which issue was most likely to decide their vote.
The top answer by some distance was health, with 22%. Second was education (9%), while war in Iraq (2%) and hunting (1%) were well down the list.
Asked which one issue in Wales specifically concerned them, people again put health top, with 26%.
Law and order (6%) was next, followed by issues to do with the assembly and education (both 5%).
Whose policies are closest to your own, no matter how you plan to vote?
Plaid Cymru: 12%
Lib Dem: 9%
Don't know: 33%
Electors from all 40 Welsh constituencies are part of a "people's forum" for the four-part series giving voters the chance to air their views.
Huw Edwards, from Llangennech near Llanelli, said: "People's Voice is an important opportunity for us as Welsh people to share our views with those who represent us.
"It is election year so anything that raises awareness of the value of our vote is, in my opinion, to be welcomed."
The programme will also follow the personal journeys of two members of the forum taking a look at issues that affect them.
The ICM poll was carried out among 1,003 adults interviewed by telephone from across Wales between 11 - 20 February.