Without being so presumptuous as to characterise the 'type' of girls who come from either the east or west end, we can assume that the songs meaning somewhat reflects the character of the west-end and east-end of London.

*Note that today, the old boundaries have been somewhat blurred by development...

**East end**

> The area was notorious for its deep poverty, overcrowding and associated social problems. 

**West end**
> The term was first used in the early 19th century to describe fashionable areas to the west of Charing Cross

So, historically, 'West-end girls' would have been upper class and stylish whereas 'East-end girls' would have been working class and (one can assume) not stylish.

  [1]: https://en.wikipedia.org/wiki/East_End_of_London
  [2]: https://en.wikipedia.org/wiki/West_End_of_London#References