First off. Pattern density kills, not energy... as long as you have enough energy to penetrate the skull/vertebrae.
Second... you should really pattern both guns. Especially if you're using heavier than lead shot.
On that note, heavier than lead is the way to go. I will likely be selling my 3.5" 12 gauge because I have zero use for it now. We're using a Remington youth model 870 20 gauge with a .555 Indian Creek choke, and #9 shot tungsten handloads. Yep, #9. #9 tungsten is equivalent in penetration (and therefore killing power) as #4 shot out past 80 yards.
Tungsten is EXPENSIVE. And you can't buy shells with it... you have to handload. Each shell that I handload costs me about $8 in components. But it's the best you can get. The combo above is getting me 260+ pellets in a 10" circle at 40 yards. I'm actually looking at getting a more open choke because the pattern is so tight at close ranges. I'm using Shotgun Insights patterning software and I ran the numbers and I have 100% kill odds out past 80 yards with this gun. I'll never shoot that far, but it's good to know that I have a very capable gun.
It's worth the cost to me. I spend more on gas than I will on shells. I can get up to two birds and my son can get one.
It's a game changer. For factory loads, I'd look at the Federal Heavyweight 7s.