And clearly transmigration plays with that as Aran'gar's new body clearly should have no ability to channel saidin at all... Regardless of strength.

INTERVIEW: Dec 5th, 2009
TGS Signing Report - kavorka (Paraphrased)
BRANDON SANDERSON
Ability to channel/souls. I think this has all been reported, but he stated definitively that the ability to channel is tied to soul. He stated definitively that the spark was not tied to the soul but could be affected by a specific body (i.e., just because you had the spark in one life, you could be reborn and just have the ability to learn.) He stated with 85% probability that strength in the Power was not tied to soul, meaning that if you were an uber channeler in one body, you could be weak in the Power in your next body.

Couple of additional quotes:

INTERVIEW: Apr, 2003
Budapest Q&A (Verbatim)
QUESTION
I have an exiting question, maybe, we heard of making the Forsaken reborn, so has the original body any reflection to the mind of the Forsaken?
ROBERT JORDAN
Well, if a Forsaken dies and is reborn naturally, through the turning of the Wheel, no.
QUESTION
If then the Dark One puts him in a new body?
ROBERT JORDAN
Oh, if the Dark One puts him in a new body, it is for all intents and purposes the same person, with a new body. It is a shift of an entire person.

MODERATOR
Here's a longish question from Linda that somehow fell in between the cracks... Part One from Linda: Since the ability to channel seems to be primarily linked to the soul, if a channeler is gentled/stilled, will this affect his/hers soul in a follow life as well, as in, will the ability to channel still be lost? Did THAT come through??
ROBERT JORDAN
No.
MODERATOR
Hmmmmm.. Linda, I TRIED.
ROBERT JORDAN
(that was the answer...the answer is no)