Pure Google experience means you get the stock ICS without a skin like HTC's Sense. I think it also means you are first for any Android OS upgrades, while other manufacturers take a bit longer to make an update available.
As for differences between the phones I'd say the camera on the Evo LTE and the better processor. I like that the Evo LTE's 3 buttons on the phone rather than on the display like Galaxy Nexus.
Oh and I think Sprint might also offer $50 with the Evo LTE to promote using Google Wallet in general with their NFC phones.. At least I hope they do