A typical 20 gauge dove load of 7/8 oz. of #8 shot will have approx. 360 pellets, a 3” .410 load will have approx. 307. Since a #8 pellet traveling 1200 fps has the same energy whether it’s shot out of a 20 or a .410, your only consideration is which choke to use. Luckily, modern .410s come with chokes (the older ones many of us shot as kids only came in ‘full’ which is why they have a reputation of being only for experts) and can regulate the pattern to match the circumstances. Briley used to have a choke pattern chart on their site and may still…it’s a great reference for this.
Just know that the patterning distance used to determine choke value for a .410 is different. It is usually based on % of pattern in a 30in circle at 25 yards. Depending on which book you read, the circle is sometimes reduced to a 25 inch circle as well. For the 20 and 12 it is based on % of pattern in a 30in circle at 40 yards. The percentage in circle used to figure the choke is the same for both the 410 and 20 despite the different distances.
So for example using the two shells presented with Modified in both shotguns, in the .410 your looking at 55-65 percent of 307 pellets in a 30 inch circle at 25 yards. Then compared to the modified in a 20 it is based on having 55-65 percent of 360 pellets in a 30 inch circle at 40 yards. You would be comparing an apple to an orange despite both shotguns having a modified choke. There is much more at play than pellet count in the shell when it comes to how choke is determined in the .410.