Well, there are two different ways (among others) that your brain detects depth:

1. Each eye sees the object from a different angle.

2. Both eyes see the object from a different angle when the object is moved relative to your head.

The 3DS does only #1. TFA does only #2. Presumably if you did both, you could get a much stronger effect.

I think the New 3DS had the hardware to do both in theory, but it probably would have made development and backwards compatibility overly complicated!