I have had difficulties with sleep mode before, but mostly because something wakes the PC up in the middle of the night or while im away for awhile, changing certain power settings i think works with that problem. Either way sleep mode is useful if your going to be away for an hour or 2, if you let it sleep overnight it might be better to shut it off entirely, but it depends on whether you want to let it boot up or just wake it up.
Your sleep mode issue could be a program not responding from sleep, have you checked Windows Task Manager for anything out of the ordinary? If you have many different programs running it might cause your slowness when you wake the computer up. You can check this from running msconfig or using CCleaner. When you shut down the PC in sleep mode do you have programs in the background (checking task manager)?
could be your problem. Or if you have outdated drivers, it couldn't hurt to run CCleaner through your computer to see if you might have something preventing Windows from waking up properly. Another last ditch effort is to try plugging your computer in a diff outlet/power surge protector.
Sadly I doubt it has anything to do with programs not coming back up properly after sleep, as I dont run anything major besides my browser, when I put the PC in sleep mode. Also nothing out of the ordinary is running in my task manager.
That I can sometimes fix the problem by changing resolution indicates it is a driver or at least graphics related issue, though I am using the very newest release from Nvidia.
Finally I also doubt power is a problem. I'm using a Seasonic 750 gold PSU, so I'm kinda naive enough to think that takes care of any shortcomings from the outlet. Besides it never was a problem earlier.
The only reason why i would think its either a PSU issue or surge protector would be a malfunction with power resume after sleep mode. Although it might not be a real issue, i was considering the fact that when a system is fully powered down no or very little power is going into the PSU & sleep mode uses more energy to power the PC in a low state so once you either touch the keyboard/mouse or hit the power button to resume it's almost like it had always been on in the first place. Again im only theorizing but electronics can be a bit weird if one thing is even slightly off voltage.
I had a hard drive that came on but did not spin up due to a bad power strip. The weird thing was that it just didn't work in a certain plug, while everything else that was hooked up was fine the plugged in hard drive did not function correctly until i tried a different outlet.
Since you did mention it might be your GPU it is possible that's your issue.. most likely it's not handling the sleep mode function. One option is to try another GPU to see if it fixes the sluggish use after it's been put to sleep.