The free app from Google is an impressive search helper, capable of searching your phone and the internet by voice, but the addition of push notifications for new Gmail messages and Calendar events in the latest update adds a nice bit of supplemental functionality that most Google die-hards will most likely love—particularly because getting true push notifications (with message previews, for example), previously required some sort of third-party tool standing in the middle.
The update also adds as-you-type search results. Google Mobile is a free app in the iTunes App Store. The update is supposed to be available now, but so far the late version hasn't shown up for me. If it's not there yet for you, either, it should be sometime today.