Is there a relationship between the jewel count of a vintage pocketwatch and its quality?
Vintage watches are completely mechanical devices with a lot of moving parts. Minimizing friction is critical in their design. Fairly early in watchmaking it was discovered that the combination of a sapphire or ruby and
hardened steel make an extremely long-lived bearing. Garnets and diamonds are also used, mostly for show. When methods of making synthetic jewels in a small donut shape were invented, around 1900, they became universal in watches. Jewels are also used in the
escapement, where again their extreme hardness lets them hold the correct shape indefinitely. In theory, a watch using more jeweled bearings could be more precise. A manufactured jewel will have a precise shape to very high tolerance. It can be made to hold oil in place and to greatly reduce friction.
In early watches jewels are also used a "caps" over pivot bearings to hold oil in place and to keep dirt out. Generally, cap and cap-less pivot jewels are the only ones that can be seen on a watch movement, without disassembly.
The idea that the use of jewels, more jewels, equates to higher quality was promoted by 20th century watch companies. The relationship is valid to an extent, but is clearly exaggerated. Synthetic sapphires and rubies are quite inexpensive to make, and so it's not unusual to see vintage watches with extraneous jewels that are really quite pointless.
Jewels have a disadvantage in that, like hardened steel, their hardness also leads to brittleness. They do not wear down like a soft metal, but they crack and break, failing catastrophically. On the other hand, it is simple to make a watch in such a way that jewels are easily replaced. But in general, a higher jeweled mechanism is likely to be less durable.