It is:
\n1.  d4    d5\n2.  c4    e6\n3. Nc3   Nf6\n

Much more concise. I don't have to keep flipping my mental image of where I'm sitting to work out where pieces are. d4 is d4 is d4. It isn't Q4 or Q5 depending on whose move.

Plus if you change languages, the algebraic change is much smaller. For instance in French it would be:
\n1.  d4    d5\n2.  c4    e6\n3. Cc3   Cf6\n

The English notation would translate into something like this:
\n1. P-D4     P-D4\n2. P-DF4    P-R3\n3. C-DF3    C-RF3\n

Which translation looks easier to learn?

Now let's translate into Spanish.
\n1.  d4    d5\n2.  c4    e6\n3. Cc3   Cf6\n

vs
\n1. P-D4     P-D4\n2. P-DA4    P-R3\n3. C-DA3    C-RA3\n

You can't even keep oriented without constantly remembering the change in names of the pieces!

The fact that Philidor liked giving long-hand descriptions has held back chess in the English-speaking world for long enough. I'm glad that everyone has switched to the simpler to learn algebraic.

Cheers,
Ben