In those days the Republicans were moderates and the Democrats were liberals (sort of). Well, if you go back to the Eisenhower era the Democrats were either liberals or Dixiecrats, who were only Democrats because they were still pissed at the Repubicans from back in the Civil War days and because the KKK never made it as a political party.
After the downfall of Nixon the Republicans party became conservative (sort of) and the Democrats became moderates.
I think that GWB is a lot more like Reagan than either to GHB. Consider how the Reagan administration botched up the deployment to Lebanon.
I think the big change to the Republican Party came between Nixon and Reagan. John Anderson (remember him?) tried to keep the Republicans in the middle but lost out. The Democrats have changed more slowly in response to the Republican change.