I don't really have a pony in this race, but logically, there is a difference. There are strict government laws in place to protect SSN information, such laws do not exist (apparently) in India regarding Aadhar. I don't think the argument is (mostly) about having a national ID, but about the lack of privacy of that information. Of course biometrics are bad in another way... If one needed to, you could change an ID number, you can't change your fingerprints
Social Security Number in the US pre-dates the internet and any concerns people had about privacy. People used to include it on their pre-printed personal checks along with their name and address.
SSNs don't even have a checksum to detect typos, nor any convenient mechanism to issue a replacement number if one is compromised.
Using the security flaws of the SSN implementation to justify security flaws in any modern identity system is just not rational. If anything it shows that people didn't learn from history.
Back when Social Security was first being put in place, there was a lot of concern that SSN's would become a "national Identification Number", and there were laws put in place to prevent this. However, said laws were largely ignored and SSN was pretty frequently used for all kinds of non-governmental purposes. In the last decade or so, there has been a renewed concern about SSN due to identity theft, and PII or Personally Identifying Information. It's now highly discouraged for anyone to store SSN numbers, although they can be still be collected for certain things like opening bank accounts and what not to prove citizenship, as well as to report to the IRS.
IMO the IRS should not be using SSN's for identification. But i'm not sure what else they can use.
> Social Security Number in the US pre-dates the internet and any concerns people had about privacy.
People in the US were concerned about privacy long before the Internet. The 4th Amendment to the US Constitution dates back to the 18th century, for example.
In fact, I'd say people are much less concerned about privacy in the Internet era; they put everything online and happily give private info to corporations and government.