As an American living (and searching the internet) in the United States, my perspective might be a bit different from that of some of you who reside in India.
Google intentionally varies search results based on a person's location. Country-specific ccTLDs like .in, .ca, and .co.uk will have an enormous advantage in achieving a high page rank within India, Canada, and the UK respectively. However, ccTLDs will suffer in page rank outside of their native country. Accordingly, .es domains will feature prominently in Spain but will tend to disappear in India; and .ca domains that rank #1 in Canada will be invisible in Spain.
The same is not true of something like .org, .net, or .com which are neutral across all locations. So a .org domain could rank high anywhere, but a .in domain will have an advantage in India (and a commensurate disadvantage outside India).
Within the United States, where the online market is very large and extremely saturated by now, .com is dominant for almost all search results. Runners up in the race are .net and .org. Beyond those 3 TLDs, it is very very rare for someone in the United States to see any other extension. Most Americans, for example, don't even know that .us exists -- even though it is technically the country code for the United States! For my part, the only times I encounter a .in domain, a .co.uk domain, a .es domain, or a .ca domain are occasionally when I am searching for very specialized phrases that pertain to the relevant country. For example, if I search for "Mumbai", on page 1 of Google I will see 7 .com domains, 1 .org domain, and 2 .gov.in domains (ranking #6 and #10). But the average American will never see a .in domain.
Meanwhile, since .org is geographically neutral and can rank okay anywhere, there is a lot more worldwide competition for .org domains than there is for .in. That means that .org domains are already registered for which the same word or phrase is available in .in -- or else the .org domain is priced much higher than the corresponding .in. As a result, .in is usually much more affordable than .org; and many more domains remain available and undeveloped.
Basically, the way I see it, .in is the domain of choice for businesses whose market is concentrated in India -- or for non-Indian businesses who want to build a website focused on an Indian audience. But for businesses that want to do business globally, .in will not be sufficient for the same reason that any country code TLD is insufficient -- namely, because of the downgrading it suffers in search results outside that country's borders.
Both .org and .in have their place, and there is very little overlap between them.
For example, Houses.org is currently parked; and the domain owner undoubtedly has priced the domain for an American buyer in the U.S. market. It wouldn't make sense for someone selling or brokering houses in India to register Houses.org because there is no need to appeal to an audience outside the country's borders and also because Houses.in would probably be cheaper AND result in an SEO advantage within India.
On the other hand, if the owner of Music.in wanted to reach an audience outside of India, he would have to invest in domains with other extensions -- non-ccTLD domains like .com, .net, .org, etc.
When considering which kind of extension to buy, the domain owner really needs to decide where the audience will be -- inside India or everywhere. In the first case, buy .in. In the second case, buy .com, .net, or .org alongside .in.