The new Opera eats less bandwidth by using a proxy and server-side compression
Very similar to the older Opera Turbo technology, and based on the Opera Mini tech and infrastructure, Off-Road uses a proxy and server-side compression to speed up browsing especially when using a poor internet connection.
It's somewhat of a stretch to call even this a new feature since it is based on the old Turbo. The only big addition is that it now uses a SPDY connection for even faster loading and more efficient use of the connection to the proxy server.
The end result is bandwidth saving that can add up. This helps if you're using a mobile connection and you have a traffic cap or if you're simply too far away from the WiFi and want pages to load faster.
It's a useful feature, but Google is already experimenting with something similar on the mobile Chrome and it's not hard to imagine that it will expand the feature to the desktop version of Chrome as well.
One other thing worth mentioning is the new download button and panel, probably the only actual new thing, new to Chrome and new to Opera. Though, of course, this new feature is almost an exact copy of the download button and panel in Firefox.
There are, of course, plenty of other new features, but all of them are sourced from Chrome. The new smartbox is a great example. While Opera's version is improved thanks to search provider switching, it is still essentially just the omnibox.