Nexus 4 (T-Mobile) vs. Galaxy S III (Verizon)

Currently on Verizon with an OG Droid and looking to upgrade to either a Nexus 4 (on T-Mobile's $30 prepaid plan) or a Samsung Galaxy S III (Verizon). While the S3 would allow me to use LTE, add storage and swap batteries, I'm pretty into the idea of stock/vanilla Android as featured on the Nexus 4.

So, two questions:

  1. Is there a way to flash Google's release of stock Android onto the GS3 or would I need to use a custom ROM like CynaogenMod?
  2. Nexus 4 users: What carrier are you on and how are the speeds you've been experiencing?