I'm not a hardware expert, but I believe the following is the answer to your key question (i.e. why don't I have the problem with Hibernate)
Hibernate actually turns off the computer, saving memory state to the hard drive before hand. Sleep just powers down some parts of the computer (I believe it typically puts the CPU into an extremely low power state while maintaining the computer state in powered-up RAM). So when you resume from Hibernate the computer goes through a full power-up sequence including all the BIOSy stuff that prepares peripherals etc. Presumably resuming from Sleep doesn't do that, since the computer wasn't powered off completely anyway.
I had issues recently with a Radeon 7750 that had exactly the same issue: that is, if the computer went to sleep, there was no display when I woke it up. I never actually got round to diagnosing it properly, and have since passed that computer on to a friend (I should probably have told hum about that issue,
tbh ). I read something somewhere that suggested having the GPU overclocked played badly with some power settings, so if your card is overclocked that might be worth looking at?