If your schedule is extremely regular then it won't save you a whole lot over a traditional programmable assuming you have it dialed in properly. It does have a few small features like Airwave that will run the fan a little longer after kicking off the furnace/compressor to get the most out of residual heat in the air handler (assuming humidity is low enough), but that isn't completely exclusive to Nest.
The Nest proximity sensors are capable of discerning pets from people.
Remote access is definitely the killer app though. It's great for days where you might only intend to be out of the house for an hour for lunch, but your lady friend ends up turning the day into an 8-hour shopping excursion. It's definitely a nice feature to have. I don't even touch the thermostat anymore; I use the website to control my thermostat if I'm hot/cold in my home office, and leave my phone on my nightstand to make any adjustments if I feel the need.
Can you please expand on your experience with the proximity sensor and auto-away.
My current thermostat is non-programmable because I moved into a new house about a month ago and they had a very basic 'stat.
I have been eyeballing the Nest for quite some time and think this is the perfect time to upgrade (since my current stat does not even allow for a schedule or programming).
My worry is that the stat is in a hallway that does not get much traffic. Our floorplan is more open and we do not walk by that area much. How close do you need to be for the proximity sensor and how would the Nest work with Auto-Away if we come home and don't make a point to walk past the thermostat?