It depends on the service. One example would be if the Mo in the 316 is there for pitting resistance (note Mo in the PRE equation) might not match it. Or if 316 is considered necessary due to the reducing nature of the medium then 309 may not be adequate again. General corrosion resistance would normally be quite similar. 309 would theoretically be better for oxidizing service. But the difference may be negligable. I would suggest consulting the design authority before unilaterally making the change.

Js55 said it better than I could.

From a weldability standpoint 309 and 309L was deisgned specifically for the of welding dissimilar metals to austenitic stainless steels. As such it readily welds to 316/316L  and I would expect no additional welding problems over the use of matching filler material.

There are corrosion resistance considerations between 316 and 309  that would need to be investigated.

may I ask why the use of 309 filler?