Several considerations when choosing a pump vs a double or auto. Outside of fit, how quickly you normally take to set your gun to fire. If you can shoulder the gun quickly without thinking about it then you can generally get the shot off sooner. For me, weight and balance of the gun effects how quickly I can shoulder it. I like 20ga on pheasants and where I hunt, non-toxic shot is required. Having a quicker first shot is more likely to prevent cripples running very far. I've shot birds on the second shot but they were usually right at the edge of the gun, choke and shot effectiveness.
I'm probably the only one who shoots a 20ga o/u in my area. If I shot a pump or auto, I would go 12ga, 3" mag #2 (currently use 3" #4). Then I could take my time to shoulder properly due to able to reach out further. There has been many times which I wished I had a 12. I've seen many shots from others bring down birds at distances which I wouldn't even attempt but I get my chances at birds, so no complaints.
Which type of gun you choose will depend upon which will feel more comfortable to you.