Fast boot is much more than keeping RAM powered up. Or, to be more accurate: it's much much less than
booting up your device from the cold. I have used fast boot option on 5.1.1 (CM12.1 unofficial for Galaxy S2 GT-I9100), and it "shuts down" in seconds, and also wakes up in seconds, but not everything is just frozen, some things "boot up" or restart after fast boot. I have observed (using OS Monitor) that there is some file system scanning after each fast boot. It could be the infamous media scanning, that occurs after storage volumes are mounted. I'm seeing it the way that the OS doesn't leave media "open" in fast boot mode. By unmounting the storage, it makes sure every read/write is completed before powering components off. I'd do it like that, but I'm no hardcore expert, so I'm basically guessing (saying this to keep it fair - don't ask me for more details, as I don't know).
The real benefit? If everything works with fast boot, the OS does not need to do full startup, load all the system components, graphics, sounds, devices, daemons... it needs for normal operation. If normal full boot takes time, be sure it consumes battery. But, how much can one or two minutes of heavier loading hurt? We're supposed to run the battery for hours in actual use. Anyway, the post-boot activity will be cut down, and definitely it's a battery saver if you don't need to have the device running for the next 30 mins plus. I would use fast boot if I was on a bus for example, without a charger, and needed to check the map or messages and then get some sleep. Or just hang out without the device
Cons?
1) Firstly, as previously stated, all the "dirt" and errors follow. If the system is overly loaded, it will be after fast boot.
Note that you still should be able to do forced full reboot by keeping power button depressed as long as the screen goes black, approx. 7 seconds on my I9100 - or just take the battery out on the fly, if it's removable. The only case when to NOT force reboot / cut the power is this:
2) I think I found a real danger with fast boot: I kinda bricked my phone yesterday. I guess I didn't wait long enough for shut down, and took battery off. I was just doing a normal shutdown, to replace the battery with a new battery! What a waste...
Doesn't boot, the phone is stuck on Cyanogen logo and sometimes flashes of "Optimizing...". I let it run for several hours, but it doesn't finish.
So, if fast boot works ok, it saves battery because a) the device doesn't boot from zero and b) it doesn't really operate being sleeping.
My EUR cents...