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The PM claimed a win for Labour would mean a "chaotic Brexit" but Mr Corbyn said the Tories were "strong against the weak and weak against the strong".
Mrs May also declined to confirm the so-called triple lock on the state pensions would be kept in place.
The SNP's Angus Robertson, who raised the issue, said the PM's answers showed she planned to "ditch" the commitment.
The triple-lock, which has been in place since 2010, guarantees that pensions rise by the same as average earnings, the consumer price index, or 2.5%, whichever is the highest.
With a general election looming on 8 June, the exchange could have been the last between Mrs May and Mr Corbyn.
Mr Corbyn opted to read out questions from members of the public, who were concerned about low wages, house prices, school spending and the NHS.
The PM defended the government's record and repeatedly said the Conservatives offered "strong and stable" leadership.