As a general rule you should use 316L filler or wire when using 316SS but of course that's is dependent on whatever the engineer calls out. Stainless steels, including the 316 series, usually have poor corrosion resistance in low-oxygen environments, such as under deposits, in mud, or in tight places, called crevices, where structures or hardware are attached. It's called Crevice Corrosion and can be prevented as long as there is water flowing passed the metal. Stainless steels get their corrosion resistance by the formation of a surface film, called the passive film, which forms on the surface in the presence of oxygen. So as long as you use the right materials you shouldn't have a problem.
The conservative approach would be to utilize the L Grade. Maybe. Keep in mind it is only going to help you in the HAZ and the weld metal where Cr carbides are likely to be formed. Also, the Mo in 316 has 3.3 times, (in the standard PREN) the pitting resistance of Cr and so 316 would still be considerably better than 308L or 304L. Also, the L Grades have a tendency to retain higher Delta ferrite, even if Ni is kicked up, (since C is a powerful austenite stabilizer- ~35X that of Ni) and the Mo Cr will be segregated at a higher level in the L grades.
Mo and Cr will move to the ferrite (these are the crevice/pitting corrosion elements) leaving less of it in the austenite (more ferrite means the Mo and Cr do not have to travel as far to find a ferrite home)
The decision comes down to expense. If the cost is close and you can absorb it, then its moot, if the cost is too high then I would try and find some corrosion studies that closely match the application. That is after all what design is all about.
If your problem is pitting/crevice corrosion then Mo may come to the forefront, if general corrosion then Cr will probably be predominant.
With this you have to assess if its hard water soft water etc.
I'm not trying to overcomplicate this thing but design is design.
If you are designing you are also accepting liability.
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