As stated above, larger bores do not compensate for poor shot placement. 40 and 45 caliber rifles have accounted for quite of lot of deer size game, not to mention tons of small game.
I have two Pedersoli's. One is the Frontier rifle in 36 cal. Sparks good and shoots good. The only issue I have with the 36 is the patent breech system Pedersoli uses. With light loads, in small bores, it's difficult to fill the chamber, even when loading more than enough powder to fill said chamber. Felt wads will push the powder to the chamber, filling the chamber most times. Even with the frustration with the breech, it still shoots very well.
IMHO, working on the basics of marksmanship will go a long way toward promoting good shot placement.
To improve your marksmanship, I suggest replacing the flint with a wooden block and dry firing in your living room. Do your practice off hand. Best done when no one is is the living room, basement, garage, or where ever. NO powder in the bore or the pan. If the rifle is a cap gun. Put a piece of rubber tube over the nipple, extending past the nipple, about an eighth to a quarter inch, to cushion the impact of the hammer against the nipple. cock your piece, as if you are firing on the range. Aim and "fire" at some prominent object in the room, such as a light switch, a spot on the wall, or some easily recognizable part of a picture, or some such.
Learn follow through by holding the rifle to a slow count of 3 or 4, after the shot breaks, and learn to call your shot, by keeping the sights aligned on your chosen "target" as and after the shot breaks. If the sights are properly aligned on the target, and you are focusing on the front sight, you should be able to see any movement of the sights, off of your chosen target. That is calling the shot. Knowing where the shot would go by keeping focus on the sights.
Live fire, on the range, only works after you have learned the basics, and can, at least, keep all of your shots on paper, at 50 yards, or so, off hand. Live fire is only used to confirm what you have done while practicing your dry fire, at home. Plus, dry fire saves a bunch of money, and allows you to see what you are actually dong, as opposed to getting distracted and blinded when dealing with the report, recoil, and smoke generated by your piece, on the range.
Good luck, good shooting, and good hunting.