As already noted, the "red"/"not red" distinction in and of itself isn't very useful, because high quality beef that has not been exposed to air will be "not red", while old, going-bad beef will also be "not red", as will properly dry-aged beef. Without a lexicon of more fine-grained descriptions of color and other characteristics of appearance, it's not possible to say in any sort of reliable, useful way how a "not red" cut of beef differs from a "red" cut.
As a general rule, I'd prefer "fresh-looking, not-red" beef over beef that has been artificially brightened with exposure to air. But neither seem particularly problematic to me. The freshness is much more important than the exact color.
More to the point: if you are using a butcher where you have any question at all about whether they'd sell you a piece of beef that isn't perfectly fresh, or they aren't willing or able to directly and accurately answer your question about why one piece is bright red while another is not and which one you should prefer (if either), you're probably at the wrong butcher.
In other words, find a good butcher, and they will be infinitely better at answering a question like the one you've asked here than we ever possibly could.
Unfortunately, in this day and age of supermarket meat cases, the concept of having trust in your retailer seems to have been lost. But there still are highly professional, customer-oriented butchers out there; it's even possible to find them at grocery stores, now and then. It's worth seeking those butchers out and giving them all of your meat-purchasing business.
With a butcher you can trust in your corner, you will over time learn first-hand what makes for a good, fresh cut of meat, and will be able to distinguish yourself between the various examples of "not red" and what they mean in terms of the quality of the cut.