I always like looking at the United States history. Back then, Democrats were for the working class with great presidents like FDR, John F. Kennedy, and Harry Truman. I respected them, even though I am Republican, but found a drastic shifty of change comparatively to the past than present.
Personally, I think Democrats are more leaning further to the left than their older groups. With more going into more Government Control, and less small time governments. With a Democrat himself, Bernie Sanders, admitting he is a Socialist. As well as other Democrats, even Hillary Clinton, having more ideas far left than partial left.
For this reason, I will agree that Democrats modernly seem more far to the left that before.
The Democrats are actually more of a center-rightist group than a far-leftist one. They compromised on Universal Healthcare, giving us the Affordable Care Act, and the Democratic President Barack Obama approved of drone strikes against terrorists and the toughest immigration laws in US history. Do I really need to say more?
With major caveat for both parties: less racist (though there are outliers - vocal ones particularly in the Republican Party, though silent ones probably exist in the Democratic Party as well). The Republicans have moved further to the right, but there has been a rise in libertarianism (capitalist style) within that party. In most other countries, that would have spawned off a new party. I agree that the Democrats, for the most part, are centre-right. In the UK, they would be called the Conservative Party. The Republican Party (moderates) would be called UKIP (nationalist-right) and the Ted Cruz', Santorums, and Trumps would be called the BNP (extremist-right - they would be monitored by MI5). Bernie Sanders would be called either Labour Party (centre-left) or Social Labour Party (the traditional labour party - left), depending on how he would implement his plans.