If those dogs are pointers you might be okay with the .410 but good shot selection is important. Seeing both guns are pumps what is the difference anyway? 12 ga shells are cheaper and you could shot 1 oz loads or less to reduce recoil. One of my favorite loads for "game farm" birds is a 1400 fps 7/8 oz load of #7 1/2 that coat a whole $3 a box. Put that in the chamber and some 6's in the magazine if you don't "focus" enough on the first shot.
Don't underestimate what it takes to drop a rooster that is flying straight away at 30 yds +.