A deep and complicated question!
Fortunately there is no paradox here, although some explanation is in order, and a clarification.
The short answer is that you can figure out the time dilation using just Special Relativity from the point of view of the lab frame, in which one of the samples is moving quickly and the other is at rest. The time dilation factor is given by
T/Tprime = 1/sqrt(1-v**2/c**2) where v is the speed of the vial in the centrifuge, and c is the speed of light.
To calculate the relative decay rates from the point of view of the accelerating
vials, you do need to use general relativity, but the ratio of the rates comes out to be the same as we just found, so there's no paradox.
The experiments which back this up are almost identical to the one you propose! They involve storing muons moving very close to the speed of light in a circular pipe with magnets all around to steer the muons around in a circle. Muons are heavy, unstable cousins of the electron. Muons decay with a precisely known lifetime, about 2.197 microseconds. The acceleration of the muons around the ring in the 1966 experiment I have access to in this context was 5x10**20 cm/sec**2, or 5x10^17 times that of gravity (a trillion times more than you suggest)! No effect was seen other than those predicted by special relativity (Farley, 1966). More precise measurements have been made since, and here at the University of Illinois, we have some of the world's experts. They have measured the time dilation factor due to the fact that the muons are moving to a few parts per million, with no evidence for any additional effect from the acceleration. An effect seen would have violated general relativity.
The time dilation in a gravitational field does not depend on the local strength of the field, but rather "how deep you are inside" one. If the gravitational field is nearly uniform, so that it is almost as strong way up high as it is near the ground, then there will still be gravitational redshift of light climbing up against gravity.
My source here is the fine book "Gravitation", by Misner, Thorne and Wheeler -- the specific case you mention is discussed on p. 1055.
Tom (and Mike)
(republished on 07/23/06)