I've been in the Odin fight on a PS3, PS4, and a PC.
Basically, on the PS3 there's not enough memory available for all the people running around and you'll have stuff not displaying. This is typical of big FATE encounters, that the PS3's memory isn't sufficient. It helps if you have a SSD in the PS3, though. The system will have less object pop-in and disappearance that way.
- FPS will be effected by the low CPU performance though, and you can expect it to be really low FPS in something like Odin.
On the PS4 there's plenty of memory and graphics performance, so you don't have problems with object pop-in and the like, but the CPU performance isn't sufficient for all the people running around. FPS can drop below 30 sometimes in big FATEs like Odin. I've had it run fairly OK, though.
- I've been in big FATEs like Odin several times, and never had a crash issue, although I'm sure it's possible, since it would push the thermal ceiling of the PS4, and if someone didn't have their PS4 in as open an area as mine, it could overheat.
My PC handles Odin well, with a 2500k OCed to just 4.2 GHz. Although, I watched CPU utilization during one smaller Odin fight, and it was getting close to max (between 87%). I've never seen any other game push the CPU anywhere close to that hard, and can say that anyone with a more modest desktop CPU, like an i3, or an AMD 8350, would probably hit a CPU bottleneck in the Odin fight, and see a FPS drop (like the PS4).