My 346XP came with an 18" bar and .325 chain, and that was good because that was what I wanted. After running a couple of gallons of gas through it here are my impressions.
I think the bar and chain size I have is the biggest I would put on this saw. I have cut up to 20" hard seasoned oak with it, but you have to pay attention to how it wants to run (wide open), and if you do it will drop right through big wood. If you don't it will quickly bog down.
I think it would actually be a happier, better saw, with a 16" .325 bar and chain.
I have never run a 3/8" chain, but it seems to me it would put more drag on the saw to pull a wider chain through the wood. The 346XP does not take well to drag, especially if it made the rpm drop. Just MHO.