I was taught with the older techniques, but I like the new chunking and gridding system better. I think it is a lot closer to how you would break the problem down if you couldn't use pen and paper and had to do everything in your head.
Incidentally, I didn't bother with a calculator until 12th grade. Since then, I've started making more mistakes, and now have to do any mental calculations several times over.
I would suspect, however, that if you habitually had to do long multiplication, the old method would be faster (precisely because you do a bit more in your head and less on paper). Multiplying two 5 digit numbers involves adding up 5 numbers instead of 25.
But what has changed over the last 40 years is that NOBODY does habitual long multiplication anymore, because calculators are ubiquitous. Therefore, the technique is purely a building step for further understanding, and picking an algorithm optimized for casual users of multiplication is appropriate.