Well. I checked a webpage talk about this.
usually, just in grammar, they have no obvious differences.
But when in different sentences, they can't be changed to each other.
If 以 is used as a conjunction in a sentence, it can't be changed to 凭
e.g. 我们要以饱满的士气迎接挑战. We will face the challenge with superb morale.
In this sentence, 以 is a conjunction. and can't be changed to 凭
another one is 我们给他们以强有力的反击, we will pay them back with strong counterstrike.
in this sentence, 以 can't be changed to 凭, either.
but if 以/凭 is used to mean "is used as...or according to", like you said, you can change it.
e.g. 西班牙以托雷斯的进球赢了德国。 Spain defeat Deutschland by Torres' goal.
西班牙凭托雷斯的进球赢了德国。 Spain defeat Deutschland by Torres' goal.
(Actually, I am fan of Deutschland..................)
I hope you can be clear with my explaination.