The point of talking about changing political competition is to explain the regional disparities that prop up in many places. So far there is the story of how that happened in the South--that the end of Democrat political dominance and the beginnings of economic growth are related--but I think this is broadly applicable in many places.
In India, you have the result that the Congress Party saw an close to their political monopoly in 1991 and many good things started around the same time. These are commonly seen as unrelated but my sense is that there is a relation. This appears to make that point, though a little dated, while this makes the argument with respect to human development indicators.
One interesting consequence of this idea is that wedge issues that break up an otherwise indifferent electorate really matter. The end of Democrat power in the South was fueled by such issues as abortion and Civil Rights, while several Indian states have seen the rise of regional parties that exploit various linguistic differences and petty concerns. The actual issues may be inconsequential, but they perhaps explain why southern Indian States--in which these issues were more salient, resulting in greater competition between the regional parties and Congress--generally developed more before 1991.
After 1991 you have the development of a plausibly national party of the Right as well as many other regional parties. It's tough to tease out the effects on the national level, but on the state level there were many differences coinciding with the growth of state-level disparities. The effects are not entirely positive, as in order to gain popularity the parties do all sorts of things such as incite violence, go for blatant populism, and so forth. The current Reddy-led Congress government in Andhra Pradesh is a great negative example of this--aside from bad populist schemes catered to every group, they went to far as to declare a cease-fire with Maoist rebels to allow them time to rearm, so now you have more violence than ever. And the anti-incumbency factor being what it is, many parties plunder as much as they wish while in office and rail against corruption once out of office.
But in a general climate of institutional decay, you do see some degree of improved state-level governance spurred by political competition within states and economic competition across states. To some degree this has happened across all parties: the current BJP governments in Gujarat, Madhya Pradesh, Rajasthan, Chhattisgarh, and Karnataka are all reasonably promising, while BJP-supported governments in Orissa and Bihar have upended both political dominance and bad governance. Bihar is a particularly good example, as former Chief Minister Lalu put together a populist majority and let the state wither away. New governance has improved conditions, while Lalu himself--pulled by the incentives of ascending to Prime Minister one day--has turned out an unexpectedly good manager of the Railway system. Meanwhile, Congress control of Delhi has turned out extremely well.
There's much, much more to this than just that. An excess of competition (this seems similar to the excess-entry argument in IO) in places such as Uttar Pradesh seems to simply make governing anarchic. When parties compete on grounds of solidarity or identity rather than issues or ideologies (no matter how apparently distant from actual conditions) there are fewer incentives for governments to perform well. The growth of the middle-class is really important as well, as parties begin to compete on the basis of their political values. There are many particular state-level dynamics--in Gujarat the BJP has simply dominated for some time and run a tight ship--that complicate issues. But the basic theme seems right to me, and also relatively unexplored in past studies.
Edit: It would be awesome if I knew the politics of more than two democratic countries.