You can simply look at a Nexus 6 and this year's Moto X to see the strong similarity between the two devices. While it may be somewhat of a disappointment to see the Nexus venture away from the design found in last year's phone and Google's two most recent tablets, there are some good things to come from this turn of events. One such nicety is the inclusion of something akin to Moto Display, formerly known as Active Display, and referred to here as Ambient Display.
On the Nexus 6, an option appears under display settings with the description "wake screen when device picked up or notifications arrive." As long as this remains enabled, notifications will appear on the screen automatically whenever new ones arrive or the phone is picked up.
The screenshot and photo below come from a leaked dump of the Nexus 6 ported to a Nexus 4.
Update: Here is a clearer image, also taken on a Nexus 4.
The Ambient Display terminology appears on the Nexus 6's Play Store page, but Google doesn't offer a description there of what it does. Instead it points out that the phone will last for up to 250 hours on standby with the feature turned on and 330 with it turned off.
This feature first appeared on last year's Moto X, and it has shipped in several Motorola devices since. This appears to be one of the perks of having the manufacturer produce the Nexus 6. For people who have grown accustomed to the functionality, the convenience is difficult to give up. If you aren't already hooked, prepare yourself.
Thanks, Connor Kirkby.