Power is mainly impacted by 1) the display, 2) the CPU, 3) the cellular radio, and 4) the OS. Newer displays tend to be more efficient per inch than older displays, so I would guess the displays on both phones would use similar power.The second is the CPU. The lower the voltage a CPU can run at, the longer it can stay at low clock speed and still get the work needed done, the deeper the standby state, and the lower the overall leakage current on the gates of the particular design/process the less power will be used. The 800 is likely more power efficient in terms of wattage/unit of work done. The Snapdragon 800 is on the newer 28nm HPm process at TSMC (the Snapdragon 600 is on the older 28nm LP process), so the amount of power both CPU's is probably around the same under most conditions, despite the names of the processes involved. The LTE radio on the 800 is a newer, more efficient one than the 600, and you can bet that this impacts your battery life when using any data. The advances in these LTE radios have brought about significant power improvements the past 2 years.
Finally, the OS is another key difference. Android, under real world use, tends to use more power than WP, mostly because there tend to be a lot more background processes running, especially when a user starts loading up on widgets. Overall, if I had to guess, I would say the 929 would probably get a lot more standby time, and probably somewhere between a half hour to an hour more talk time and similar for data. This phone should easily last through a day of moderate use. Proof will be in the pudding.