The latest Reuters/Ipsos MORI poll of marginal seats - constituencies narrowly held by the ruling Labour party - shows that voters rate Labour leader Gordon Brown more highly than Cameron on almost all leadership measures.
However, the poll also shows nearly 60 percent of voters want a leader who represents change.
It is a dilemma that helps explain why the country is still on course for a so-called hung parliament in which the Conservatives are the largest party but fall short of an overall majority in the 650-seat House of Commons.
"Many voters in these key marginals do think that the Conservatives are ready to govern and that Cameron is ready to be Prime Minister, but a significant minority still have their doubts," said Ipsos MORI's Helen Coombs.
Ipsos MORI polled 1,008 adults between March 30 and April 5 in key marginals: seats the Conservatives must win if they are to secure an outright win in the May 6 election.
It found 37 percent of those polled believed Gordon Brown best understood the problems facing Britain compared to 30 percent who said Cameron. Forty-one percent thought Brown would be best in a crisis compared to 30 percent who said Cameron.
Brown was seen as having a better understanding of world problems and a better grasp of detail than his Conservative opponent, and was ahead on questions of who was the most capable leader. In national polls, Cameron is seen as the most capable.
Despite Brown's relatively strong showing in the marginals, the poll showed that after 13 years of Labour rule, the country wants change: the central message of the Conservative party who have adopted "Vote for Change" as their campaign slogan.
When asked if Britain needed a Prime Minister who brought fresh thinking and a new approach to secure economic recovery or one who could draw on past experience, 57 percent opted for the fresh approach while 40 percent said experience.
Commuters at Chatham rail station in Kent -in the marginal constituency of Chatham and Aylesford - shared the mixed feelings toward the leaders.
"The country needs a change of direction and Cameron seems a little more in control," Keith Walker, an engineer, told Reuters.
But Gary Pinder, the director of a small business who has not yet decided which way to vote, said: "David Cameron lacks substance. His qualities are still to be proven.
"Given everything that has happened, he should be 20 percent ahead by now. Cameron's back-up team also don't seem as strong as they should be." A survey of economists conducted by Reuters last month showed they would rather have Conservative shadow business spokesman Ken Clarke as Chancellor than shadow Chancellor George Osborne. An Ipsos MORI national poll in February found that, for the first time since 1987, leaders were as important as policies in helping people decide who to vote for.
This means Britain's first ever televised leaders' debates could make a significant difference, particularly as nearly half of voters have not yet made a final decision on how to vote.
Some 46 percent of those polled in marginals say they may change their mind about who to vote for and 60 percent say the debates will be important in helping them decide how to vote. The three debates will be held on April 15, 22 and 29.
Overall voting intentions are little changed from the last Reuters/Ipsos MORI poll two weeks ago.
Some 38 percent of voters said they would vote Conservative at the next election - up from 37 percent last time - and compared to 41 percent who said they would vote Labour.
That represents a 5.5 percent swing to the Conservatives from Labour compared to the last general election in 2005. The Conservatives need a swing of 6.9 percent nationally to gain a majority in the House of Commons.
