ESTA - Las Vegas - My experience.
Went from LGW - LAS June this year with Virgin. We were issued with Green Forms at the baggage drop in Gatwick. On board, my wife made a couple of errors in filling these cards in. Ask the CC for replacements to be told that they weren`t required for Las Vegas, and that the USA was introducing a rolling programme of doing away with said cards. We did have to complete Customs Form.
On arrival, and at immigration, I noticed that we seemed to be the only ones who weren`t clutching their green cards.
Anticipating some questions at the control gate, I handed my passport over along with the customs form. Security didn`t even bat an eyelid , but did all the usual iris scan and fingerprint stuff, stamped our passports and welcomed us to the States. No issues either on the way home at departures.
Iain