Since it's a backpacking trip, especially a BSA one, the type of backpacking you want to do affects your decision the most. Sure, you want to go light. But will the Scouts be cooking in one big group or splitting into buddies (buddies, most likely)? If the water purification will be done as a group, a 7 oz filter/pump is usually best. Only one person has to carry the weight, and it can do big amounts of water relatively quickly.
Drops are fine, but doing 10 liters of drops twice a day starts to cost money and you go through drops quickly that way. Tabs are even more expensive. A steripen per each buddy system would work well because it's a little monotonous to Steripen 10 separate liters with one steripen a couple times a day, not to mention you'll go through batteries much faster than you'll go through a filter.
So a filter, for the same cost and weight of the $60 Steripen, will last longer, serve big groups more efficiently, and weigh almost as little as a Steripen (arguably less when batteries are included, but filters have accessories, too). It will take a little while, but realistically just about as long as it would take to individually hit all those liters with UV light, or as long as it would take to wait for chemicals to take effect. And only one person has to carry it.