I can see where both of these techniques are beneficial for researching. Close reading makes me think of dissecting a body of work. You as a scholar want to understand what the author is trying to get across, with every word. I did not know how close you could get to a piece of work until we did our in class exercise. Looking over the sonnet that Shakespeare wrote, Dr. Pandora showed me that you can focus on many different aspects and can even spend months or years on one. For example, she said you can focus on a phrase and analyze it for months at a time. Months for a few words! If this skill is honed, it can be very powerful in research.
Like I said earlier, I think distant reading has value as well. If you do not know what you are looking for, skimming through multiple pieces of literature in an attempt to understand it enough to know if it is useful can be productive. Researchers can waste a lot of time reading material that may or may not pertain to the topic they are working on. Digitally, these skills can be amplified greatly. Using a computer to search for key words or phrases among thousands of documents can be a great tool. Sometimes it may even allow you to discover works that you may have never uncovered. However, this could make the researcher lazy because it can be seen as the computer doing most of the work.
Now, I do think that these two techniques can work together. You may start out distant reading to find relevant material or material that is interesting. Then, you can take a closer work to analyze the piece more closely to understand it. I think this is something that researchers are already engaged in because of the huge amount of material that is in the world. Like Ramsey says, there is no way that anyone could come close to reading everything in the world, which is why it is important to hone these skills.
If I were to choose one of the techniques over the other, I would probably choose close reading. My reasoning is that you actual get to the heart of the material and try to understand what the author was trying to say. I think you learn more when you actually understand the piece of literature more.