One standard answer to this question is that a better widget is a widget that conforms more closely to the specification for widgets. The specification defines an ideal widget. If we can make our actual widget to be a very close reflection of that ideal, then we have a better widget.
The usual first step in this improvement process is to quantify the various facets of widget specification so we can measure how close the actual widget is to the ideal. If we adjust the operation of our widget factory, we can then compare the new widgets with the old widgets. If the new widgets give measurements that show less deviation from the ideal, then we have produced better widgets. And of course there are statistics involved. The actual widgets we produce are not all quite the same: some are very close to ideal, some are further off. The whole process of improvement can get quite complex, but it can be driven by statistical measurement and managed quite effectively.
Another sort of better widget is a redesigned widget. We can change the specification. What does it mean for one specification to be better than another?
One way to think about this is to notice that widgets serve some purpose, have some use. Very commonly, widget A is used in the process of manufacturing widget B. Our process for manufacturing widget B is a better process if the resulting actual widget B conforms more closely to its specification. So a better widget A is one that produces a better widget B.
In judging the specification for widget A, we would like to know how well an perfect widget A would function. Some actual widget A might produce a poor quality widget B, but just because widget A itself is of poor quality, i.e. does not conform well to its own specification. The fault is not in the specification.
So we have two notions of quality or of improvement: design and manufacturing. An improved manufacturing process will produce actual widgets that conform more closely to their specification. An improved design will specify widgets that can improve the manufacturing processes in which they are used.
This framework brings up many further questions. The network of widgets, where widget A is used to make widget B, is quite vast. Are there widgets that are actually useless, whose value cannot be measured by their effectiveness in some application? What happens when there are loops in the network, so that the notions of better and worse become (indirectly) self-referential and therefore potentially unstable, ambiguous, etc.?
Another problem occurs because a widget might have multiple uses. A new specification might be better for one use but worse for some other use. Perhaps we really need two different types of widget… but then we lose the savings from economies of scale.
At the limit, in a custom construction situation, the processes of design and manufacturing processes are not clearly distinguished. Widget B is designed and manufactured for just a single use. We may be able to measure the quality of widget B through its effectiveness in its application. But we cannot clearly distinguish the quality of the specification of widget B from the quality of the manufacturing process that produced widget B. So, for example, if we used widget A to produce widget B, measuring the quality of widget A becomes problematic.