Well, this is a pretty classic breakfast conundrum. On one hand, SSU offers maximum yolk yield, easy penetration and is aesthetically appealing, hearkening back to a simpler time and giving breakfast a more dynamic palate with the sharp contrast the yellow offers . EOE provides an ( I know I’m going to get flamed for this) better texture and a deeper, richer tasting yolk (from the extra cooking time), but smaller overall liquid yield . Now, while both have merits on their own, I think you can only discuss SSU vs EOE in the context of accompanying dishes. I firmly believe if you want to solo it, you should go for scrambled, but that’s a whole other post.
To start off, 99 percent of the time this is going to be served with toast. Most likely on a 1-1 bread/egg ratio. While this is common, your toasted surface area (TSA) will vary from bread to bread as will the amount of liquid yolk (LY) from egg to egg. Figuring out your TSA to LY is essential to maximizing yolk use. Generally, my rule of thumb is TSA>LY=SSU and LY>TSA=EOE. When I know I’m going to be working with large amounts of toast, I’ll often spring for a medium light roast, low butter texas white to maximize absorbency. When dealing with small amounts of LY yolk, I’d recommend an ultralight roast heavy butter rye which will accentuate the flavors and synergize your dipping.
But what about beyond the dipping phase? No yolk is an endless bottom. This is where I think EOE really shines. While SSU has just depleted itself, EOE bounces back into the meal, there, cooked reserves of solidified yolk remain to delight the senses. With SSU, you seem to peak within 3 minutes. EOE is just getting started. The yolk adds unfathomable amounts of texture, complexity and depths to any kind of pairing/combination (such as toast, bacon etc). While SSU is not bad post dip, it lacks sophistication.
Of course, this is all my opinion, and I haven’t even begun to really consider tetrary and quadratic accompaniments, like bacon and pancakes. These can affect the foodscape in both vast and subtle ways. What is the spread on your bacon/sausage option select? Will egg yolk possibly compromise your syrup pool? Have the eggs been strategically placed on top hash browns?
These are all questions you will have to struggle with, and unfortunately, there is no clear answer. Many great thinkers have struggled with the notion of the sublime breakfast, and very few have ever mastered it. Ultimately, we are stuck with the ever so imperfect trial and error, and ultimately, we are shaped and forced to live by our decisions. Don’t let anybody tell you how to enjoy your eggs, life is too short and precious for that.