The 'European' model is not a wealthy centre and poor outskirts (that's the prototype Third World city), but traditionally was a wealthy centre, a ring of working class areas (aka the Inner City, with usually an upper class district thrown in), then the middle class suburbs.
Of course all that has been upended due to house prices as the middle classes and rich now colonise the Inner City ring, and the working class sell on at profit and become middle class suburbanites. Meanwhile the classy mansion districts subdivide to make it more profitable for the upper middle classes to take over in higher densities. This is seeing a current half-way house of rich and poor and middle class mixing that's a tradition since Victorian property speculation.
An apartment in a former council estate tower block, and one in a subdivided former 20 bed mansion both sell for the same price ($500,000). Your neighbour on one side may be working class, on the other upper class.
This is why there is currently White, Caribbean, Jewish and South Asian 'flight' away from the centre and into the suburbs as the last generation cashes in for leafy suburbia, while new arrivals from the world's rich take their place (aristocracy, Arabs, French, Chinese, Italians, Indians, Nigerians, Russians). Of course their children will probably move back into the city starting the whole cycle again, so ongoing the mixing.
In the future there won't really be large tracts of working class districts any more, though anything on the peripherals may well turn out that way - in other words a transformation toward a natural Third World set up of a rich centre, middle class suburbs/ inner city, and working class peripherals, though more mixed still (for decades all new developments, even luxury ones, have to have a proportion - as high as 30-50% under Mayor Livingstone - devoted to affordable housing).