Do batteries last longer with constant current draw or spiky current draw?
This is a very good question and I don't have a good (complete) answer.  So I'll just give you a tidbit one of my old bosses used in a design.  There is a certain type of battery with very high internal resistance that he used for a long-life application.  Since it's high resistance, it has low leakage and its charge won't dissipate well on its own, but you can't source a lot of current from it.  Since it was a periodic application (similar to yours) he paired it with a supercapacitor.  The cap would charge up and when the uC was ready it would turn on, perform its actions.  

But for the life of me I can't remember the words he used to describe it.  I've tried searching for low leakage, high internal resistance and other terms I thought it was but I can't seem to find exactly it.  It wasn't a coin cell, but more like a AA (but it certainly wasn't that form factor).  I perused the Wikipedia article in Lithium batteries and the closest I could find was the Lithium-Iodide battery.  There's plenty of info in that article as well:

http://en.wikipedia.org/wiki/Lithium_battery

Many different chemistries and a comparison table.  Good read.

Good luck!