Big bore will, with nothing else changed, give i think something like 3~ more hp, but that really depends on the kit.
The con is expense and downtime. The old downside was that you couldn't clean it up, like a small step up if it grenaded, you had to get another set of cylinders or go real big. Some older ones consumed more oil but nowadays they don't. 836 won't have heating problems either, you haven't gone big enough yet to bring that deal on.
You likely won't have to change jetting because the engine breathes a little more efficient and sucks more fuel thru those jets. Think the reverse of the pod effect, sort of. Some guys have dropped to 38 pilots, but all are a little different.
If you want to go balls out then send the head to Mrieck. That will be a different build tho, that starts to get more serious tho he does offer reconditioning, you don't have to go crazy. Is tempting tho. If you want to go low budget with a healthy engine then lap the valves in and slap it together.
I am one of the ebay 836 guys so I have first hand experience with some of the changes. Others can chime in too. I rebuilt my 836 outside (no garage/shed/anything convenient lol), more or less basic hand tools and I took it down to the point of splitting the cases. If you aren't ham fisted and can follow pictures and directions you are fine. It seems like a joke but really, the text is important not just the pretty pictures. I wish PO's would read more a lot of the time.