Back to the technical issues of your question, YES, a poor shot with a BIG gun will be better and more effective than a POOR shot with a small gun, and that is the way your question is phrased. A heavy gun is more likely to have an exit wound and leave a blood trail.
That being said, a poor shot is a poor shot. I have never lost a wounded deer. OK. I will say that again. I have NEVER lost a wounded deer. I have come close, had to track a few, but not many. Some people doubt that, but it is so.
I have shot 1, ONE , deer running. That is out of about 85 or so deer I have killed. Three or four were walking. The one running was the one and only one I have ever shot with a 270 Win, and I have never seen more damage than that shot did.
Every other deer I have taken has been with a 35 or larger caliber. I would say that there is no replacement for shot placement. One mistake that I think many may make is their point of aim. Most have been drilled continually with trying for a double lung shot. The deer I came closest to losing was a yearling that I shot broadside with a 44 mag super blackhawk. He ran almost a 1/4 mile and we looked for an hour and a half for him. When we found him there was a hole that you could have dropped a golf ball all the way through him, both lungs. It was impossible for him to run that far, but no one told him that. I made a point after that, unless they are in clear territory to aim high in the shoulder. It may not kill as fast, but it is an anchor shot, most likely taking out the spine , and damaging the shoulders to where they cannot run. The spine shot usually sends bone fragments through the upper lungs, esophagus and jugular vein, so death is relatively rapid, just not instant. If you are in brush where tracking is tough, take the shoulder/ spine shot. I have put more deer down right there with that shot, using a 444, than any other.