316S/Steel has Molybdenum (Mo) added to give it more pitting resistance than 304. As such it is usually a more expensive material. As Mo is a very strong ferrite stabiliser, some of the Cr is removed, and extra Ni added to keep the material austenitic. In many applications, it does not make a big difference which one of the two grades you use. There are some applications where the extra pitting resistance is absolutely essential. There are also some applications where the extra Mo and less Cr of the 316 makes it a "worse" material than the 304. (e.g. Nitric acid service.)

In short, I believe that many people think 316 is "superior" because it costs more, but as with just about all materials, you need the right one for the job. In some cases this will be 304 and in some cases 316. (In some applications C/Steel gives a much better service than any stainless steel, so which material is the better material?)

Regarding the fillers, the correct grade should be used for the particular application. Usually this means using 316 for welding 316 base metal, and 308 for welding 304 base metal. If you are using 304 because you need its particular properties, welding it with 316 would lead to an inferior joint.