Dear Megan,
I've listened to both videos and must say the change between the two videos is very evident. In the second video, despite the hoarseness and softness that's still there due to the healing process, the voice has a much lighter quality that is much more feminine than the old one. It is true, however, that the basic timbre hasn't changed a lot, which seemingly is the case with all of Dr. Kim's patients. Jenny also reported that the voice remains identifiable, with just the bottom end removed.
So don't let anybody scare you or tell you differently, the surgery was a success and you'll see the full benefit of it a few months down the road when the healing has progressed, the Botox worn off and the swelling fully gone down.
Best wishes for a speedy and full recovery,
Amy