I don't think a 12 would be cheaper to shoot. Most times they are about the same price.
I didn't look at the specs of the gun, but I would guess the 12 is heavier. Even if they are built on the same frame the 12 will be a lot more muzzle heavy normally. I have 2 12 gauge guns, and one 20. The 12's are a really nice 1100, and a Mossberg 500. The 20 is a beat up savage 67 pump. The 20 gauge see the light of day way more than the 12's.
Put it this way. I probably hunted small game about 10-12 days this year. The 500 still has the slug barrel attached from last year (2 minute swap). The 1100 made it out once, and only because I figured I should use it. It was the first time in about 3-4 years. I remembered after about a mile of walking why I never use it.
I'm thinking that the 20 will get one more walk tomorrow.