Both of these towns would be family-friendly, but I would have to say that Windham may have more to offer an active family. It's more than twice the size of Atkinson (about 25 square miles vs. about 10 square miles for Atkinson).
Atkinson (like many small towns in NH) has a volunteer fire department, while Windham has full time paid firefighters.
Windham also has an active rec. department, including summer activities at the pond in town. (I'm unsure of what Atkinson offers for rec. activities) And if you're in doubt of the number of children in town, be sure to make it to the annual Windham Strawberry Festival that benefits the library. It's a blast!
Lastly, Windham runs it's own school system. Currently the HS students are tuitioned to Salem, but Windham is building their own HS this year. Atkinson students (all grades) are part of Timberlane District.
Hope this is some helpful info to get you started