The experience of a Developer Edition phone is the closest you can get to a Nexus on a non-Nexus device. Basically, it is "Vanilla Android", just like a Nexus, but optimized/recoded to fit a different hardware and, in some cases, some added stuff needed to take advantage of the new hardware. For instance, the M8 with its dual cameras had to ship with a specially modified version of the camera to take advantage of the two lenses (the stock Nexus one having only one sensor to worry about), but the rest of the software is pretty much the same.
However, updates are generally delivered to Nexus devices first. Why? Google controls those. Once that is released, then other manufacturers need to adapt it to their own phones. With Developer Editions, however, the wait is usually not as long as with customized implementations.