There isn't really a difference between these two approaches, in the end the result is the same.
If you think of SSN as your node key, I'd say it's better to use NODE KEY because it's shorter and expresses what you mean, rather than implying what you mean with constraints.
Separately -- just a tip from someone who has done data modeling for years -- SSN is not a good key for database systems, because it isn't unique. This is surprising, but true. If you have a small customer base, maybe you won't ever run into this, but if you grow, you for sure will.
Another weirdness of SSNs that trip a lot of people up -- they can have letters behind them. People think they must always be 123-45-6789 but that's not correct. The value 123-45-6789aa is a valid SSN.
The reason I mention this is that using SSN as a key in a database is a rather classic "gotcha" problem that crops up later.