IMac :: Swap Out Screen Or Complete Replacement Of Computer?

I have the 27'" Imac with slight yellow tint on bottom and grey bar shadow running along the bottom as well. Additionally, the buzzing sound when brightness lowered below 50%. The computer works great otherwise and I don't hear buzzing when at normal distance from screen. My dilemma: Apple has offered to send a technician to my home to replace the screen, and they said that whould also fix the buzzing noise at lower brightness at the same time.
My question is have people been satisified or had better luck with screen replacements rather than simply asking for a new computer in exchange. If I'm simply swapping displays to get the same results, or even exchanging computer to only get the same results or worse, I would rather delay this interaction until a real fix is in place. My current Imac has no dead pixels, and works great except for these issues. HD makes a grumbling noise, but I think WD Black Caviars are known to be a bit noisy.
Any advice on way to go would be appreciated. Swap out display? Exchange computer? Stand pat?