As a long time Nvidia buyer, and one admittedly looking towards a 300 series AMD when they're released, I'll bring up my issues with questions like this one.
The first is that answering a question like this offers no real-world application. You're asking people to examine this question in a vacuum, and that's just not realistic in regards to how we operate as humans. We will always, whether subconsciously or consciously, be evaluating things against multiple variables. So, what's the point of asking this question? Are you trying to provoke the AMD apologists, or hoping for an admittance that Nvidia and Intel make better products?
The second issue is individual bias (which you've done a terrible job of hiding in framing your question). Although, to you, you feel that your experiences with Nvidia or Intel have been better overall, this doesn't hold true for everyone. A few of my friends have been die-hard AMD supporters (to the point where we give each other shit over drinks for choosing the obviously inferior choice). They haven't had all the issues that you see people bring up on forum discussions every time someone drops the words "AMD" and "Nvidia" in the same sentence. There are so many variables which can impact performance. I've had some terrible experiences with certain Nvidia drivers and GPU combinations. Some have had terrible experiences with AMD drivers and GPU combinations. Most discussions I see regarding these driver issues where blanket statements are made don't offer any factual tests that would classify those statements as anything other than speculation based on individual experiences.
It's not rare to see people claim AMD drivers are bad and then find other posts made by them admitting they've never owned an AMD product.
The third issue is that products like Pepsi and Coke are, arguably, static products. I.e., they're not frequently evolving/changing. In a blind taste test, you're looking at two specific products. In the question that you posed, you don't even specify two specific products. Which combination of hardware are we discussing? Are we talking about the current high-end graphics cards offered by both companies paired with the same CPU? Are we talking about SLI and CrossFire configurations? Are we using liquid cooling? Air cooling? What about the PSU? Or the motherboard? These products, unlike a can of Pepsi and Coke, are not static. They're constancy changing. So, when we're comparing the cards, are we really going to compare a 2013 card against ones released in late 2014? Is that truly a fair evaluation of technology? What would the implication of your question be if you were asking it a few months from now when the 300 series AMD comes out? Nvidia and AMD aren't necessarily neck-to-neck competitors. They leap-frog each other in terms of product cycles and launches, thus, at least for now, you're not going to have two cards that you could truly, fairly compare between the two.
The fourth is the reality that corporate deals do affect performance. When Nvidia, or AMD for that matter, offer money or decide to do bundles or promotions with a developer, it's just more likely that the game will be better optimized for that particular company. So, your question, for it to be fair to both, would need to assume equal optimization for both cards. I'd also argue that they would need to have the same software advantages, e.g. something like PhysX that was open source and available for both. I think this issue really demonstrates that your vacuum situation isn't practical. See, it's due to corporate systems (like promotions that Nvidia has with certain developers) that push them to incorporate Nvidia specific software applications, like PhysX.
The fact is that you can't do a Pepsi test between the products you desire to. The vacuum that you desire can't exist, because we don't know what it would look like if it did.