The US were a blank page, with roughly the same crowd starting with the same common goal and aspirations. Europe comes with 15centuries of nationlike structures and history. Latin and AngloSaxons have very different approaches on life and work (particularly visible in the “PIGS” recent controversy...).
As someone said, you cant make the european omelette with nations hard boiled eggs.
The mere facts that the euro bank notes has zero european symbol (because they couldnt find one) speaks for itself. So they put bridges and windows... India has Gandhi.
"Anglo-Saxons" are not part of the federation anymore, and stuff like "PIGS" is simply casual racism. Do Northern European countries have a casual-racism problem? Very much so. Would that stop a federation from working in the long run? I doubt it very much. Otherwise Texas and New Jersey would have parted ways a long time ago.
Also, comparing diversity is tricky - natives from Lappland have 0 in common with say Greek or Spaniards. Same would go for india's extremes, its rather impossible to say who is more different (personally I would still say Europe, since ways of life are almost the same if you look on India east, south, north, west, very similar cuisine etc... not so much in Europe).
We have proven track of how it doesn't work here in Europe, no need to spin another set of wars to re-confirm it.
Also, India sees quite a bit of domestic terrorism in its eastern parts exactly due to mindsets like yours. Not something we like to see here in Europe.