The ballistics on the ammo charts are almost all for 24" barrels...which drives me nuts because fewer 24" barrels were made compared to the 20". The 16" trapper is slower still. No factory load is going to steamroll anything from a trapper, but both the 150 and 170 gr bullets will work just fine. Win 150 gr Powermax bonded worked well when I shot them. It's kind of a hollowpoint, so I dont think I'd use them for bears but on deer it's a great load.
The Hornady 160 Lever Evolution load is one that I've shot from a 20", and it is a velocity improvement over standard, so that might make up a touch of the velocity loss from the trapper tube, and the bullet weight is right in the middle. I'd use this on either.
For the bears at short range, especially a 300 pounder needing deep penetration, try the Federal Nosler partition 170 grainers.