It would only be a guess on my part, but the presence or absense of a barrel band probably won't make a huge difference one way or the other......Just guessing, the barrel band would be more prone to accuracy problems than the gun not having a barrel band.
I wouldn't let the barrel band be the deciding factor, but if you find one is more cosmetically appealing, carries better, or there is a significant difference in price, then go with ever gun you like the best and makes the most sense to you.............
Generally, you can expect around 2" groups, and with a little tweeking and or handloads you can probably get it down to just over an inch.
Some of the marlins people post about will do better than an inch.
I have 2, an 1895 in 45.70 with a 1.75 X 6 leupold and it's best group has been right at an inch, but it's very consistant and average groups are just over that. it doesn't have a barrel band.
My other is a 336C in .35 remington, no scope but with a ghost ring and I get 5 shot groups at 50 yard that will average about an 1 and a half....I suspect that with a scope it would do better, but where I hunt a scope is not really an asset and 1.5 inches is plenty good enough. It has the barrel band and I find that I like the long tube with the barrel band as it has a more traditional look.
No right or wrong answer on either gun, but more personal preference.
Which one do you like the best?