Just use nails if you can. The screws are for if you can't get a hammer on something, but you might be able to get a screw in somewhere. I actually found this more useful on some shear nail holes where I was up against a header for my stairs on my deck.
Screws are pricey, so nails would be your first choice. but, if for some reason you can get a screw in a hole you can't get a nail in.
Use the #9 or #10 screws screws depending on the type of nails you are replacing. Most likely the #9 are all that will fit in your devices.
This all depends on what type of strong tie connectors you are using. Based on your lumber dimensions we are all guessing it will be 10d nails. BUT PLEASE VERIFY WITH YOUR specific case.
By the way, use the recommendations given to you for your application. Bigger is not better. I actually called the strong tie rep when I was building my deck because I was getting **** information from "experts". A few of there connectors call for 8d for face nailing and 10d for the double shear nails.
I called the rep to ask/inform him about lowes and HD not selling the correct nails. Only carrying the shorter face nails and guys telling people they were the right ones for all the holes. Rep sounded a bit miffed and aware of the issue. Ended up talking to their engineer.
Anyway, I asked him why they would use 8d and 10d on one design and not just call for the 10d all around. I thought it would make it a hell of alot easier on folks like me and probably easier on their supply chain and stocking distributors/retailers.
He told me they actually tested them to try that and found the smaller nails in the pattern they are in actually bested the larger nails in the pattern they would have to be in for pullout strength.
