I've recently needed a new pair of eyeglasses. My glass lenses had been (very slightly) scratched a while ago, and what this ultimately began leading to was for the protective film on the lens to begin a slow process of infinitesimal flaking and cracking. Because the process was so slow, it wasn't generally noticeable. However, not long ago I was finding myself a bit bothered as to how my lenses were catching the light, and I remembered that I had an old pair of back-up glasses from a previous prescription and dug them out to see how they would work, and it was extraordinary. I had been seeing through what was effectively a cloud; now, everything was much clearer.
The interesting thing, of course, is that the prescription on the back-up glasses is an older, less adequate prescription. The lenses I had been using are a somewhat better fit for my eyes than these older glasses, and under very specific circumstances (the lighting just right) this can be seen. But in general, the cloudiness created by the deterioration of the lenses makes the better-prescription glasses worse than the glasses with a less adequate prescription.
This strikes me as an analogy for how methods of inquiry often work in practice. Just as the more defective lenses with more adequate prescription can be less effective than the less defective lenses with less adequate prescription, so too a more adequate method that is used in a way involving inadequate understanding can be worse than a less adequate method that is used with good understanding. In fact, I think that, when people talk about 'common sense' in arguing and reasoning, they are often talking about this phenomenon. A method might be very powerful, but used badly might be worse than a much simpler, more modest method used well. Many people obviously go wrong by applying methods they only poorly understand, and in many fields you get people who develop elaborate structures on sophisticated methods that are less adequate than simpler structures built on less sophisticated methods, even where the methods used in the elaborate case are, considered in themselves, better methods.
There are obvious constraints about how this would work, some of which can be seen in the analogy. For instance, it's obvious that one reason you can have this result in the eyeglass case is that the eyeglasses are doing the same thing and have the same purpose, so they can be directly compared. In appealing to 'common sense', people sometimes err by directly comparing things that in fact have different ends in inquiry; this is not an error exclusive to common sense (people do it with massively more sophisticated and expertise-requiring methods, as well), but it's a possible error that has to be kept in mind.
Another condition is that we are dealing with a matter in which approximation, in a broad sense, can be practically useful. That is, in fact, what we are talking about, really; lacking a perfectly understood perfect method, we are comparing methods that have imperfections, or at least limitations, and that are therefore already might not be adequate for high-precision, high-accuracy work. Neither the defective better-prescription glasses nor the effective worse-prescription glasses get me out of having to get an eye exam and new glasses; it's just that in comparing these two glasses, neither of which is perfect, the unclouded weaker prescription is an improvement over the clouded better prescription. Likewise with methods of argument and reasoning.
A third condition is that the difference cannot be very extreme, as measured by its relation to the end in view. Obviously glasses that are so scratched up nothing can be seen are bad glasses whatever the prescription; obviously glasses whose prescription is so off that they are useless are bad glasses whatever the condition of the glasses themselves. As we approach either, we are getting worse; it's just that the approach to each is distinct, and therefore one is not always worse than the other. Of course, if you have a method used with complete incompetence, it does not matter how good the method itself is; and if you have a method too simplistic to get even in the neighborhood of the right kind of answer, it does not matter how competently you use it. Examples of failures on each score are easy to find in almost any intellectual field; you can go on internet forums and find examples of each with remarkably little difficulty. How things go down in between these is the more interesting and less straightforward matter.
Nonetheless, these conditions are not especially difficult to achieve. There are lots of intellectual situations in which you will get farther with a simpler approach than a more adequate approach, as long as the simpler approach is still adequate enough, simply because the simpler approach is less 'in the way' and fiddly than the more adequate approach. Sophisticated methods often come with the weakness of having hidden restrictions, hidden limitations, hidden assumptions that have to be satisfied, like cracks and flakes in the protective coating of a lens, which cannot really be seen but make the whole thing give a clouded result -- and, indeed, the clouded result might not even usually be noticeable despite always being there. How many analytic philosophers have gone wrong simply by mistranslating things into and out of the predicate calculus, making mistakes they would have avoided entirely just by using basic syllogisms or natural-language rules of thumb? More than a few. This is not an indictment of the best methods of analysis used well; but the best methods of analysis can in various ways be harder to use well than simpler methods that will get you close enough. What's more, even in using the stronger method, you might need to check your results using the weaker method; this is a common thing in fields like mathematics, and there have been times, like the early development of the calculus, when entire subfields operated entirely under this regime of always checking the more powerful and precise approach by looser or less rigorous or more approximate means.
