I was very lucky and was offered both the NSF and the NDSEG this year. I am a graduating Bachelor in Math / Physics and enrolling in a Ph.D. Physics program in the fall.
Many people have asked this question before, but it seems this year the NDSEG is significantly more than it has been in the past, so here are the details:
NSF
$34,000/year for three years ($2,833/month)
Deferable
Health insurance provided by school
Up to $12,000 provided for tuition
NDSEG
$38,400/year for three years ($3,200/month)
NON-deferable
Up to $1,200 in health insurance
$5000 travel allowance (not per year, this is for the total tenure)
Full tuition and fees covered. Paid directly to the school.
I have also accepted a fellowship from my university that will cover my first and fifth years, though I've been told I can defer it to cover my fourth and fifth instead, so it shouldn't conflict with the NSF. In regards to prestige, though the NSF is more well-known, I've been informed by my former supervisor that hire-by-name is very common with NDSEG at research labs, much moreso than with NSF.
I'm leaning heavily towards NDSEG, but just want to hear some opinions to make sure I'm not missing something.
Thanks!