A lot less than before, though some of my customers send me convos letting me know the item arrived and they are happy with it. Since I had a fair number of sales and positive feedback before the new reviews method started, it hasn't hurt me and shouldn't affect my rating much.
The ones I feel sorry for are the newer Etsy sellers who hadn't had a chance to build up a fair amount of good feedback before the new method went into effect. It will be so much harder for them to do it now, with the new system works. Also, as another seller mentioned, due to the delay between the purchase date and allowed review date, many customers will be busy and ignore the review message when they get it. Because of this, I personally don't see anything positive in the new method.